In the present paper, we study the shifted hypergeometric function f(z)=z2F1(a,b;c;z)f(z)=z_{2}F_{1}(a,b;c;z) for real parameters with 0>a≤b≤c0>ale ble c and its variant g(z)=z2F2(a,b;c;z2)g(z)=z_{2}F_{2}(a,b;c;z^2). Our first purpose is to solve the range problems for ff and gg
本文研究了实参数为 0 > a ≤ b ≤ c 0>ale ble c 时的移位超几何函数 f ( z ) = z 2 F 1 ( a , b ; c ; z ) f(z)=z_{2}F_{1}(a,b;c.) f(z)=z_{2}F_{1}(a,b;c.)和它的变体 g ( z ) = z 2 F 2 ( a , b ; c ; z 2 ) g(z)=z_{2}F_{2}(a,b;c;z^2) 。我们的第一个目的是解决 Ponnusamy 和 Vuorinen [Rocky Mountain J. Math. 31 (2001),pp.]Ruscheweyh, Salinas and Sugawa [Israel J. Math. 171 (2009), pp. mathbb {C}setminus [1,+infty ) 并在参数的一些假设下证明了 f f 的普遍星象性。然而,除了 b = 1 b=1 的情况之外,还没有系统地研究过移位超几何函数的普遍凸性。我们的第二个目的是在参数的某些条件下证明 f f 的普遍凸性。
{"title":"Universal convexity and range problems of shifted hypergeometric functions","authors":"Toshiyuki Sugawa, Li-Mei Wang, Chengfa Wu","doi":"10.1090/proc/16849","DOIUrl":"https://doi.org/10.1090/proc/16849","url":null,"abstract":"<p>In the present paper, we study the shifted hypergeometric function <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f left-parenthesis z right-parenthesis equals z 2 upper F 1 left-parenthesis a comma b semicolon c semicolon z right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>z</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mi>F</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>a</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> <mml:mo>;</mml:mo> <mml:mi>c</mml:mi> <mml:mo>;</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">f(z)=z_{2}F_{1}(a,b;c;z)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for real parameters with <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"0 greater-than a less-than-or-equal-to b less-than-or-equal-to c\"> <mml:semantics> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>></mml:mo> <mml:mi>a</mml:mi> <mml:mo>≤</mml:mo> <mml:mi>b</mml:mi> <mml:mo>≤</mml:mo> <mml:mi>c</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">0>ale ble c</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and its variant <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"g left-parenthesis z right-parenthesis equals z 2 upper F 2 left-parenthesis a comma b semicolon c semicolon z squared right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>z</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mi>F</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>a</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> <mml:mo>;</mml:mo> <mml:mi>c</mml:mi> <mml:mo>;</mml:mo> <mml:msup> <mml:mi>z</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">g(z)=z_{2}F_{2}(a,b;c;z^2)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Our first purpose is to solve the range problems for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f\"> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding=\"application/x-tex\">f</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"g\"> <mml:semantics> <mml:mi>g</mml:mi> <mml:annotation encoding=\"application/x-tex\">g</mml:annotation","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this note, we prove that the compactly supported mapping class group of a surface containing a genus 33 subsurface has no realization as a subgroup of the homeomorphism group. We also prove that for certain surfaces with order 66 symmetries, their mapping class groups have no realization as a subgroup of the homeomorphism group. Examples of such surfaces include the plane minus a Cantor set and the sphere minus a Cantor set.
{"title":"Non-realizability of some big mapping class groups","authors":"Lei Chen, Yan Mary He","doi":"10.1090/proc/16860","DOIUrl":"https://doi.org/10.1090/proc/16860","url":null,"abstract":"<p>In this note, we prove that the compactly supported mapping class group of a surface containing a genus <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3\"> <mml:semantics> <mml:mn>3</mml:mn> <mml:annotation encoding=\"application/x-tex\">3</mml:annotation> </mml:semantics> </mml:math> </inline-formula> subsurface has no realization as a subgroup of the homeomorphism group. We also prove that for certain surfaces with order <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"6\"> <mml:semantics> <mml:mn>6</mml:mn> <mml:annotation encoding=\"application/x-tex\">6</mml:annotation> </mml:semantics> </mml:math> </inline-formula> symmetries, their mapping class groups have no realization as a subgroup of the homeomorphism group. Examples of such surfaces include the plane minus a Cantor set and the sphere minus a Cantor set.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
<p>Given a field <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K"> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding="application/x-tex">K</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, a rational function <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="phi element-of upper K left-parenthesis x right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>ϕ</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>K</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">phi in K(x)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and a point <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="b element-of double-struck upper P Superscript 1 Baseline left-parenthesis upper K right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>b</mml:mi> <mml:mo>∈</mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant="double-struck">P</mml:mi> </mml:mrow> <mml:mn>1</mml:mn> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>K</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">b in mathbb {P}^1(K)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we study the extension <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K left-parenthesis phi Superscript negative normal infinity Baseline left-parenthesis b right-parenthesis right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>K</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mi>ϕ</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mi mathvariant="normal">∞</mml:mi> </mml:mrow> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>b</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">K(phi ^{-infty }(b))</mml:annotation> </mml:semantics> </mml:math> </inline-formula> generated by the union over <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding="application/x-tex">n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of all solutions to <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="phi Superscript n Baseline left-parenthesis x right-parenthesis equals b"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>ϕ</mml:mi> <mml:mi>n</mml:mi> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>b</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">phi ^n(x) = b</mml:annotation> </mml:semantics> </mml:math> </inline-for
给定一个域 K K ,一个有理函数 ϕ ∈ K ( x ) phi in K(x) ,以及一个点 b ∈ P 1 ( K ) b in mathbb {P}^1(K) ,我们研究扩展 K ( ϕ - ∞ ( b ) ) K(phi ^{-infty }(b)) 由 ϕ n ( x ) = b phi ^n(x) = b 的所有解的 n n 的联合产生,其中 ϕ n phi ^n 是 ϕ phi 的第 n 个迭代。我们问当 K ( ϕ - ∞ ( b ) ) 的有限扩展时 K(phi ^{-infty }(b)) 可以包含某个 m ≥ 2 m geq 2 的所有 m m -power 单整根,并证明这发生在几个有理函数族中。一个有启发性的应用是理解当 K K 是 Q p mathbb {Q}_p 的有限扩展且 p p 除以 ϕ phi 的阶数时的高斜率滤波,尤其是当ϕ phi 是后极限(PCF)时。我们证明,对于新的迭代扩展族,例如那些由具有周期临界点的双临界有理函数给出的迭代扩展族,所有较高的斜切群都是无限的。我们还给出了迭代扩展的新例子,这些迭代扩展的子扩展满足更强的夯实理论条件,即算术剖分性。我们猜想,由 PCF 映射产生的每个迭代扩展都应该有一个具有这种更强性质的子扩展,这将给出 PCF 映射的森定理的动力学类似物。
{"title":"Roots of unity and higher ramification in iterated extensions","authors":"Spencer Hamblen, Rafe Jones","doi":"10.1090/proc/16825","DOIUrl":"https://doi.org/10.1090/proc/16825","url":null,"abstract":"<p>Given a field <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K\"> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding=\"application/x-tex\">K</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, a rational function <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"phi element-of upper K left-parenthesis x right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>ϕ</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>K</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">phi in K(x)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and a point <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"b element-of double-struck upper P Superscript 1 Baseline left-parenthesis upper K right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>b</mml:mi> <mml:mo>∈</mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">P</mml:mi> </mml:mrow> <mml:mn>1</mml:mn> </mml:msup> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>K</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">b in mathbb {P}^1(K)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we study the extension <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K left-parenthesis phi Superscript negative normal infinity Baseline left-parenthesis b right-parenthesis right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>K</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:msup> <mml:mi>ϕ</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mi mathvariant=\"normal\">∞</mml:mi> </mml:mrow> </mml:msup> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>b</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">K(phi ^{-infty }(b))</mml:annotation> </mml:semantics> </mml:math> </inline-formula> generated by the union over <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n\"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding=\"application/x-tex\">n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of all solutions to <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"phi Superscript n Baseline left-parenthesis x right-parenthesis equals b\"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>ϕ</mml:mi> <mml:mi>n</mml:mi> </mml:msup> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>b</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">phi ^n(x) = b</mml:annotation> </mml:semantics> </mml:math> </inline-for","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider a nonstationary random walk on a compact metrizable abelian group. Under a classical strict aperiodicity assumption we establish a weak-* convergence to the Haar measure, Ergodic Theorem and Large Deviation Type Estimate.
{"title":"Ergodic theorem for nonstationary random walks on compact abelian groups","authors":"Grigorii Monakov","doi":"10.1090/proc/16848","DOIUrl":"https://doi.org/10.1090/proc/16848","url":null,"abstract":"<p>We consider a nonstationary random walk on a compact metrizable abelian group. Under a classical strict aperiodicity assumption we establish a weak-* convergence to the Haar measure, Ergodic Theorem and Large Deviation Type Estimate.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study the global dynamics of epidemic network models with standard incidence or mass-action transmission mechanism, when the dispersal of either the susceptible or the infected people is controlled. The connectivity matrix of the model is not assumed to be symmetric. Our main technique to study the global dynamics is to construct novel Lyapunov type functions.
{"title":"Global dynamics of epidemic network models via construction of Lyapunov functions","authors":"Rachidi Salako, Yixiang Wu","doi":"10.1090/proc/16872","DOIUrl":"https://doi.org/10.1090/proc/16872","url":null,"abstract":"<p>In this paper, we study the global dynamics of epidemic network models with standard incidence or mass-action transmission mechanism, when the dispersal of either the susceptible or the infected people is controlled. The connectivity matrix of the model is not assumed to be symmetric. Our main technique to study the global dynamics is to construct novel Lyapunov type functions.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate polynomials that satisfy simultaneous orthogonality conditions with respect to several measures on the unit circle. We generalize the direct and inverse Szegő recurrence relations, identify the analogues of the Verblunsky coefficients, and prove the Christoffel–Darboux formula. These results should be viewed as the direct analogue of the nearest neighbour recurrence relations from the theory of multiple orthogonal polynomials on the real line.
{"title":"Szegő recurrence for multiple orthogonal polynomials on the unit circle","authors":"Rostyslav Kozhan, Marcus Vaktnäs","doi":"10.1090/proc/16811","DOIUrl":"https://doi.org/10.1090/proc/16811","url":null,"abstract":"<p>We investigate polynomials that satisfy simultaneous orthogonality conditions with respect to several measures on the unit circle. We generalize the direct and inverse Szegő recurrence relations, identify the analogues of the Verblunsky coefficients, and prove the Christoffel–Darboux formula. These results should be viewed as the direct analogue of the nearest neighbour recurrence relations from the theory of multiple orthogonal polynomials on the real line.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We establish some ΦPhi-moment inequalities for noncommutative differentially subordinate martingales. Let ΦPhi be a pp-convex and qq-concave Orlicz function with 1>p≤q>21>pleq q>2. Suppose that xx and yy are two self-adjoint martingales such that yy is weakly differentially subordinate to xx. We show that, for
我们建立了一些非交换微分隶属马丁格的 Φ Phi -时刻不等式。设 Φ Phi 是一个 p p -凸且 q q -凹的 Orlicz 函数,其值为 1 > p ≤ q > 2 1>pleq q>2 。假设 x x 和 y y 是两个自相关的马丁格尔,且 y y 是 x x 的弱微分隶属。我们证明,对于 N≥0 Ngeq 0 , τ [ Φ ( | y N | ) ] ≤ c p , q τ [ Φ ( | x N | ) ] , begin{equation*}.tau big [Phi (|y_N|)big ]leq c_{p,q}tau big [Phi (|x_N|)big ], end{equation*} 其中常数 c p , q c_{p,q} 是 p = q p=q 时的最佳阶。本文还得到了非交换微分隶属马丁格的平方函数的 Φ Phi -动量估计。我们的方法提供了非交换 Φ Phi -矩 Burkholder-Gundy 不等式和 Burkholder 不等式的构造证明。
{"title":"Φ-moment inequalities for noncommutative differentially subordinate martingales","authors":"Yong Jiao, Mohammad Moslehian, Lian Wu, Yahui Zuo","doi":"10.1090/proc/16847","DOIUrl":"https://doi.org/10.1090/proc/16847","url":null,"abstract":"<p>We establish some <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Phi\"> <mml:semantics> <mml:mi mathvariant=\"normal\">Φ</mml:mi> <mml:annotation encoding=\"application/x-tex\">Phi</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-moment inequalities for noncommutative differentially subordinate martingales. Let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Phi\"> <mml:semantics> <mml:mi mathvariant=\"normal\">Φ</mml:mi> <mml:annotation encoding=\"application/x-tex\">Phi</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=\"application/x-tex\">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-convex and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"q\"> <mml:semantics> <mml:mi>q</mml:mi> <mml:annotation encoding=\"application/x-tex\">q</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-concave Orlicz function with <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"1 greater-than p less-than-or-equal-to q greater-than 2\"> <mml:semantics> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>></mml:mo> <mml:mi>p</mml:mi> <mml:mo>≤</mml:mo> <mml:mi>q</mml:mi> <mml:mo>></mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">1>pleq q>2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Suppose that <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"x\"> <mml:semantics> <mml:mi>x</mml:mi> <mml:annotation encoding=\"application/x-tex\">x</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"y\"> <mml:semantics> <mml:mi>y</mml:mi> <mml:annotation encoding=\"application/x-tex\">y</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are two self-adjoint martingales such that <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"y\"> <mml:semantics> <mml:mi>y</mml:mi> <mml:annotation encoding=\"application/x-tex\">y</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is weakly differentially subordinate to <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"x\"> <mml:semantics> <mml:mi>x</mml:mi> <mml:annotation encoding=\"application/x-tex\">x</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We show that, for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" al","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141516638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study a class of kk-Hessian equations, we can deduce an Obata-type formula and a Liouville-type theorem by integration by parts.
本文研究了一类 k k -Hessian 方程,通过分式积分,我们可以推导出 Obata 型公式和 Liouville 型定理。
{"title":"An Obata-type formula and the Liouville-type theorem for a class of K-Hessian equations on the sphere","authors":"Shujun Shi, Peihe Wang, Tian Wu, Hua Zhu","doi":"10.1090/proc/16857","DOIUrl":"https://doi.org/10.1090/proc/16857","url":null,"abstract":"<p>In this paper, we study a class of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k\"> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=\"application/x-tex\">k</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-Hessian equations, we can deduce an Obata-type formula and a Liouville-type theorem by integration by parts.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141530933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We establish a general framework for representability of a metric group on a (well-behaved) class of Banach spaces. More precisely, let Gmathcal {G} be a topological group, and Amathcal {A} a unital symmetric C∗C^*-subalgebra of UC(G)mathrm {UC}(mathcal {G}), the algebra of bounded uniformly continuous functions on Gmathcal {G}. Generalizing the notion of a stable metric, we study Amathcal {A}-metrics δdelta, i.e., the function
我们建立了在一类(良好的)巴拿赫空间上度量群的可表示性的一般框架。更确切地说,让 G mathcal {G} 是一个拓扑群,而 A mathcal {A} 是 U C ( G ) mathrm {UC}(mathcal {G}) 的有界对称 C ∗ C^* - 子代数,即 G mathcal {G} 上有界均匀连续函数的代数。从稳定度量的概念出发,我们研究 A mathcal {A} -metrics δ delta , 即、函数 δ ( e , ⋅ ) delta (e, cdot ) 属于 A mathcal {A};在 A = W A P ( G ) mathcal {A}=Whskip -0.7mm Ahskip -0.2mm P(mathcal {G}) 的情况下,G 上弱几乎周期函数的代数 恢复稳定。如果 G G 的拓扑由左不变度量 d d 引起,我们证明当且仅当 d d 均匀等价于左不变 A mathcal {A} -度量时,A mathcal {A} 决定 G mathcal {G} 的拓扑。作为一个应用,我们证明了 C [ 0 , 1 ] 的加法群 C[0,1] 不可反身表示;这是 Megrelishvili [Topological transformation groups: selected topics, Elsevier, 2007, Question 6.7] 的一个新证明(这个问题早在 G [0 , 1] C[0,1] 中就由 Megrelishvili 解决了)。(费里和加林多 [Studia Math. 193 (2009), pp. 99-108] 用不同的方法解决了这个问题,后来雅科夫、贝伦斯坦和费里 [Math. Z. 267 (2011), pp.129-138] 对结果进行了推广)。现在让 G (mathcal {G})是一个度量群,并假设 A ⊆ L U C ( G ) mathcal {A} subseteq mathrm {LUC}(mathcal {G}) , G (mathcal {G})上有界左均匀连续函数的代数,是一个独元 C ∗ mathrm {LUC}(mathcal {G})。 是一个一元 C ∗ C^* -代数,它是 G 在 F (mathscr {F} 的成员)上的表示的系数的均匀闭包。 其中,F 是一类在 ℓ 2 ell _2 -direct sums 下封闭的巴拿赫空间。我们证明,当且仅当 G嵌入到 F 的一个成员的等几何群中时,A 才决定 G 的拓扑结构。 的等几何群中,并配备弱算子拓扑。作为应用,我们得到了单元可表示性和反射可表示性的特征。
{"title":"Representations of groups on Banach spaces","authors":"Stefano Ferri, Camilo Gómez, Matthias Neufang","doi":"10.1090/proc/16499","DOIUrl":"https://doi.org/10.1090/proc/16499","url":null,"abstract":"<p>We establish a general framework for representability of a metric group on a (well-behaved) class of Banach spaces. More precisely, let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper G\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"script\">G</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathcal {G}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a topological group, and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper A\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"script\">A</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathcal {A}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> a unital symmetric <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Superscript asterisk\"> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:msup> <mml:annotation encoding=\"application/x-tex\">C^*</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-subalgebra of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper U normal upper C left-parenthesis script upper G right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mi mathvariant=\"normal\">U</mml:mi> <mml:mi mathvariant=\"normal\">C</mml:mi> </mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mrow> <mml:mi mathvariant=\"script\">G</mml:mi> </mml:mrow> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathrm {UC}(mathcal {G})</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, the algebra of bounded uniformly continuous functions on <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper G\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"script\">G</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathcal {G}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Generalizing the notion of a stable metric, we study <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper A\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"script\">A</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathcal {A}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-metrics <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"delta\"> <mml:semantics> <mml:mi>δ<!-- δ --></mml:mi> <mml:annotation encoding=\"application/x-tex\">delta</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, i.e., the function <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"delta left-parenthes","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let QQ be a probability measure on a finite group GG, and let HH be a subgroup of GG. We show that a necessary and sufficient condition for the random walk driven by QQ on GG to induce a Markov chain on the double coset space H∖G/HHbackslash G/H is that Q(gH)Q(gH) is constant as gg ranges over
设 Q Q 是有限群 G G 上的概率度量,设 H H 是 G G 的一个子群。我们证明,由 Q Q 在 G G 上驱动的随机游走在双余弦空间 H ∖ G / H Hbackslash G/H 上诱发马尔科夫链的必要条件和充分条件是,Q ( g H ) Q(gH) 随着 g g 在 G G 中 H H 的任何双余弦上的范围而恒定。我们得到的这个结果是一个关于双余集 H ∖ G / K Hbackslash G / K 的更一般的定理的推论,即 K K 是 G G 的一个任意子群。作为一个应用,我们研究了 r r -top 到随机洗牌的变体,我们证明它在 S y m n mathrm {Sym}_n 的 S y m r × S y m n - r mathrm {Sym}_r times mathrm {Sym}_{n-r} 的双余弦上诱导了一个不可还原、循环、可逆和遍历的马尔可夫链。诱导行走的过渡矩阵具有显著的频谱特性:我们可以找到它的不变分布和特征值,从而确定它的收敛速度。
{"title":"A necessary and sufficient condition for double coset lumping of Markov chains on groups with an application to the random to top shuffle","authors":"John Britnell, Mark Wildon","doi":"10.1090/proc/16853","DOIUrl":"https://doi.org/10.1090/proc/16853","url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper Q\"> <mml:semantics> <mml:mi>Q</mml:mi> <mml:annotation encoding=\"application/x-tex\">Q</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a probability measure on a finite group <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H\"> <mml:semantics> <mml:mi>H</mml:mi> <mml:annotation encoding=\"application/x-tex\">H</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a subgroup of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We show that a necessary and sufficient condition for the random walk driven by <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper Q\"> <mml:semantics> <mml:mi>Q</mml:mi> <mml:annotation encoding=\"application/x-tex\">Q</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> to induce a Markov chain on the double coset space <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H minus upper G slash upper H\"> <mml:semantics> <mml:mrow> <mml:mi>H</mml:mi> <mml:mi mathvariant=\"normal\">∖</mml:mi> <mml:mi>G</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">Hbackslash G/H</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is that <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper Q left-parenthesis g upper H right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>Q</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>g</mml:mi> <mml:mi>H</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">Q(gH)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is constant as <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"g\"> <mml:semantics> <mml:mi>g</mml:mi> <mml:annotation encoding=\"application/x-tex\">g</mml:annotation> </mml:semantics> </mml:math> </inline-formula> ranges over ","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}