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A family of homogeneous operators in the Cowen–Douglas class over the poly-disc 多盘上Cowen-Douglas类中的齐次算子族
IF 0.8 3区 数学 Q2 MATHEMATICS Pub Date : 2022-05-18 DOI: 10.4064/sm220630-10-1
Prahllad Deb, S. Hazra
We construct a large family of positive-definite kernels $K: mathbb{D}^ntimes mathbb{D}^n to mbox{M} (r, mathbb C)$, holomorphic in the first variable and anti-holomorphic in the second, that are quasi-invariant with respect to the subgroup $mbox{M"ob} timescdotstimes mbox{M"ob}$ ($n$ times) of the bi-holomorphic automorphism group of $mathbb{D}^n$. The adjoint of the $n$ - tuples of multiplication operators by the co-ordinate functions on the Hilbert spaces $mathcal H_K$ determined by $K$ is then homogeneous with respect to this subgroup. We show that these $n$ - tuples are irreducible, are in the Cowen-Douglas class $mathrm B_r(mathbb D^n)$ and that they are mutually pairwise unitarily inequivalent.
构造了一大族正定核$K: mathbb{D}^n乘以mathbb{D}^n到mbox{M} (r, mathbb C)$,它们在第一个变量上是全纯的,在第二个变量上是反全纯的,它们对于$mathbb{D}^n$的双全纯自同构群$mbox{M b}$ ($n$次)的子群$mbox{M b}$是拟不变的。乘法算子的n元组与希尔伯特空间上由K决定的坐标函数的伴随是关于这个子群齐次的。我们证明了这些$n$ -元组是不可约的,它们属于Cowen-Douglas类$ mathm B_r(mathbb D^n)$,并且它们是相互两两酉不等价的。
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引用次数: 0
Compactness in Lipschitz spaces and around Lipschitz空间及其周围的紧性
IF 0.8 3区 数学 Q2 MATHEMATICS Pub Date : 2022-05-09 DOI: 10.4064/sm221020-16-3
J. Gulgowski, P. Kasprzak, Piotr Ma'ckowiak
The aim of the paper is to characterize (pre)compactness in the spaces of Lipschitz/H"older continuous mappings acting from a compact metric space to a normed space. To this end some extensions and generalizations of already existing compactness criteria for the spaces of bounded and continuous mappings with values in normed spaces needed to be established. Those auxiliary results, which are interesting on their own since they use a concept of equicontinuity not seen in the literature, are based on an abstract compactness criterion related to the recently introduced notion of an equinormed set.
本文的目的是刻画Lipschitz/H空间中的(预)紧性从紧致度量空间到赋范空间的较老的连续映射。为此,需要对赋范空间中有值的有界和连续映射的空间的现有紧致性标准进行一些扩展和推广。这些辅助结果本身就很有趣,因为它们使用了在L中看不到的等连续性概念ature是基于与最近引入的二分形式集合的概念相关的抽象紧致性准则。
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引用次数: 1
A continuous-parameter Katznelson–Tzafriri theorem for algebras of analytic functions 解析函数代数的连续参数Katznelson–Tzafriri定理
IF 0.8 3区 数学 Q2 MATHEMATICS Pub Date : 2022-04-28 DOI: 10.4064/sm220428-13-10
C. Batty, D. Seifert
. We prove a continuous-parameter version of the recent theorem of Katznelson–Tzafiri type for power-bounded operators which have a bounded calculus for analytic Besov functions. We also show that the result can be extended to some operators which have functional calculi with respect to some larger algebras.
.我们证明了最近关于幂有界算子的Katznelson–Tza fi ri型定理的连续参数版本,该算子具有解析Besov函数的有界演算。我们还证明了这个结果可以推广到一些算子,这些算子对于一些较大的代数具有函数演算。
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引用次数: 2
Transfinite almost square Banach spaces 超限几乎平方巴拿赫空间
IF 0.8 3区 数学 Q2 MATHEMATICS Pub Date : 2022-04-28 DOI: 10.4064/sm220517-4-11
Antonio Avil'es, Stefano Ciaci, Johann Langemets, A. Lissitsin, A. R. Zoca
. It is known that a Banach space contains an isomorphic copy of c 0 if, and only if, it can be equivalently renormed to be almost square. We introduce and study transfinite versions of almost square Banach spaces with the purpose to relate them to the containment of isomorphic copies of c 0 ( κ ), where κ is some uncountable cardinal. We also provide several examples and stability results of the above properties by taking direct sums, tensor products and ultraproducts. By connecting the above properties with transfinite analogues of the strong diameter two property and octahedral norms, we obtain a solution to an open question from [8].
.已知Banach空间包含c0的同构副本,当且仅当,它可以等价地重定为几乎平方。我们引入并研究了几乎正方形Banach空间的有限形式,目的是将它们与c0(κ)的同构副本的包含联系起来,其中κ是一些不可数基数。我们还通过取直和、张量积和超积给出了上述性质的几个例子和稳定性结果。通过将上述性质与强直径二性质和八面体范数的反式有限类似物联系起来,我们从[8]中获得了一个开放问题的解。
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引用次数: 2
Extremal bounds for Dirichlet polynomials with random multiplicative coefficients 随机乘法系数Dirichlet多项式的极值界
IF 0.8 3区 数学 Q2 MATHEMATICS Pub Date : 2022-04-07 DOI: 10.4064/sm220829-6-3
Jacques Benatar, Alon Nishry
For $X(n)$ a Steinhaus random multiplicative function, we study the maximal size of the random Dirichlet polynomial $$ D_N(t) = frac1{sqrt{N}} sum_{n leq N} X(n) n^{it}, $$ with $t$ in various ranges. In particular, for fixed $C>0$ and any small $varepsilon>0$ we show that, with high probability, $$ exp( (log N)^{1/2-varepsilon} ) ll sup_{|t| leq N^C} |D_N(t)| ll exp( (log N)^{1/2+varepsilon}). $$
对于$X(n)$a Steinhaus随机乘法函数,我们研究了随机狄利克雷多项式$$D_n(t)=frac1{sqrt{n}}sum_{nleq n}X(n,n)n^{it},$$的最大大小,$t$在不同范围内。特别地,对于固定的$C>0$和任何小的$varepsilon>0$,我们以高概率证明了$$exp((log N)^{1/2-varepsilon})llsup_{|t|leq N^C}|D_N(t)|llexp($$
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引用次数: 1
Gromov hyperbolicity in the free quasiworld. I 自由拟世界中的Gromov双曲性。我
IF 0.8 3区 数学 Q2 MATHEMATICS Pub Date : 2022-03-04 DOI: 10.4064/sm210825-7-3
Qingshan Zhou, S. Ponnusamy
With the aid of a Gromov hyperbolic characterization of uniform domains, we first give an affirmative answer to an open question arisen by Väisälä under weaker assumption. Next, we show that the three-point condition introduced by Väisälä is necessary to obtain quasisymmetry for quasimöbius maps between bounded connected spaces in a quantitative way. Based on these two results, we investigate the boundary behavior of freely quasiconformal and quasihyperbolic mappings on uniform domains of Banach spaces and partially answer another question raised by Väisälä in different ways.
借助于一致域的Gromov双曲刻画,我们首先在较弱的假设下对Väisälä提出的一个开放问题给出了肯定的答案。接下来,我们证明了Väisälä引入的三点条件对于在有界连通空间之间获得拟Möbius映射的拟对称性是必要的。基于这两个结果,我们研究了Banach空间一致域上自由拟共形和拟双曲映射的边界行为,并以不同的方式部分回答了Väisälä提出的另一个问题。
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引用次数: 5
On subspaces whose weak$^*$ derived sets are proper and norm dense 关于弱$^*$导集是适当且范数稠密的子空间
IF 0.8 3区 数学 Q2 MATHEMATICS Pub Date : 2022-03-01 DOI: 10.4064/sm220303-29-4
Zdenvek Silber
We study long chains of iterated weak∗ derived sets, that is sets of all weak∗ limits of bounded nets, of subspaces with the additional property that the penultimate weak∗ derived set is a proper norm dense subspace of the dual. We extend the result of Ostrovskii and show, that in the dual of any nonquasi-reflexive Banach space containing an infinite-dimensional subspace with separable dual, we can find for any countable successor ordinal α a subspace, whose weak∗ derived set of order α is proper and norm dense.
我们研究了子空间的迭代弱*导集的长链,即有界网的所有弱*极限的集,以及倒数第二个弱*导集合是对偶的适当范数稠密子空间的附加性质。我们推广了Ostrovski的结果,证明了在包含具有可分对偶的无穷维子空间的任何非拟自反Banach空间的对偶中,我们可以为任何可数后继序数α找到一个子空间,其阶α的弱*导集是适当的且范数稠密的。
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引用次数: 0
Asymptotic expansion of the nonlocal heat content 非局部热含量的渐近展开
IF 0.8 3区 数学 Q2 MATHEMATICS Pub Date : 2022-02-23 DOI: 10.4064/sm220831-26-1
T. Grzywny, Julia Lenczewska
Let $mathbf{X}={X_t}_{tgeq 0}$ be a L'evy process in $mathbb{R}^d$ and $Omega$ be an open subset of $mathbb{R}^d$ with finite Lebesgue measure. In this article we consider the quantity $H(t)=int_{Omega} mathbb{P}^x (X_tinOmega^c) , mathrm{d}x$ which is called the heat content. We study its asymptotic expansion for isotropic $alpha$-stable L'evy processes and more general L'evy processes, under mild assumptions on the characteristic exponent.
设$mathbf{X}={X_t}_{tgeq 0}$是$mathbb{R}^d$中的一个L维过程,$Omega$是具有有限Lebesgue测度的$mathbb{R}^d$的一个开子集。在本文中,我们考虑数量$H(t)=int_{Omega}mathbb{P}^x(x_tInOmega^c),mathrm{d}x$,称为热含量。在特征指数的温和假设下,我们研究了各向同性$alpha$稳定的L’evy过程和更一般的L’vey过程的渐近展开式。
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引用次数: 0
Classification results fornonsingular Bernoulli crossed products 非奇异Bernoulli叉积的分类结果
IF 0.8 3区 数学 Q2 MATHEMATICS Pub Date : 2022-02-15 DOI: 10.4064/sm220217-11-5
S. Vaes, Bram Verjans
We prove rigidity and classification results for type III factors given by nonsingular Bernoulli actions of the free groups and more general free product groups. This includes a large family of nonisomorphic Bernoulli crossed products of type III$_1$ that cannot be distinguished by Connes $tau$-invariant. These are the first such classification results beyond the well studied probability measure preserving case.
我们证明了自由群和更一般的自由积群的非奇异伯努利作用给出的III型因子的刚性和分类结果。这包括一大类类型为III$_1$的非同构伯努利交叉乘积,这些乘积不能用Connes$tau$不变量来区分。这是在经过充分研究的概率测度保持情况之外的第一个这样的分类结果。
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引用次数: 0
A strong Borel–Cantelli lemma for recurrence 递归的一个强Borel-Cantelli引理
IF 0.8 3区 数学 Q2 MATHEMATICS Pub Date : 2022-02-15 DOI: 10.4064/sm220216-2-7
T. Persson
ABSTRACT. Consider a mixing dynamical systems ([0, 1], T, μ), for instance a piecewise expanding interval map with a Gibbs measure μ. Given a non-summable sequence (mk) of non-negative numbers, one may define rk(x) such that μ(B(x, rk(x)) = mk. It is proved that for almost all x, the number of k ≤ n such that Tk(x) ∈ Bk(x) is approximately equal to m1 + . . . + mn. This is a sort of strong Borel–Cantelli lemma for recurrence. A consequence is that
摘要考虑一个混合动力系统([0,1],T, μ),例如一个Gibbs测度为μ的分段展开区间映射。给定一个非负数的不可和数列(mk),可以定义rk(x)使得μ(B(x, rk(x)) = mk。证明了对于几乎所有的x, k≤n的个数使得Tk(x)∈Bk(x)近似等于m1 +…+锰。这是递归的一种强Borel-Cantelli引理。结果就是
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引用次数: 3
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