<div><div>Our concern is with Riemannian symmetric spaces <span><math><mi>Z</mi><mo>=</mo><mi>G</mi><mo>/</mo><mi>K</mi></math></span> of the non-compact type and more precisely with the Poisson transform <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>λ</mi></mrow></msub></math></span> which maps generalized functions on the boundary ∂<em>Z</em> to <em>λ</em>-eigenfunctions on <em>Z</em>. Special emphasis is given to a maximal unipotent group <span><math><mi>N</mi><mo><</mo><mi>G</mi></math></span> which naturally acts on both <em>Z</em> and ∂<em>Z</em>. The <em>N</em>-orbits on <em>Z</em> are parametrized by a torus <span><math><mi>A</mi><mo>=</mo><msup><mrow><mo>(</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>></mo><mn>0</mn></mrow></msub><mo>)</mo></mrow><mrow><mi>r</mi></mrow></msup><mo><</mo><mi>G</mi></math></span> (Iwasawa) and letting the level <span><math><mi>a</mi><mo>∈</mo><mi>A</mi></math></span> tend to 0 on a ray we retrieve <em>N</em> via <span><math><msub><mrow><mi>lim</mi></mrow><mrow><mi>a</mi><mo>→</mo><mn>0</mn></mrow></msub><mo></mo><mi>N</mi><mi>a</mi></math></span> as an open dense orbit in ∂<em>Z</em> (Bruhat). For positive parameters <em>λ</em> the Poisson transform <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>λ</mi></mrow></msub></math></span> is defined and injective for functions <span><math><mi>f</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>N</mi><mo>)</mo></math></span> and we give a novel characterization of <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>N</mi><mo>)</mo><mo>)</mo></math></span> in terms of complex analysis. For that we view eigenfunctions <span><math><mi>ϕ</mi><mo>=</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>(</mo><mi>f</mi><mo>)</mo></math></span> as families <span><math><msub><mrow><mo>(</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>a</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>a</mi><mo>∈</mo><mi>A</mi></mrow></msub></math></span> of functions on the <em>N</em>-orbits, i.e. <span><math><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>a</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mi>ϕ</mi><mo>(</mo><mi>n</mi><mi>a</mi><mo>)</mo></math></span> for <span><math><mi>n</mi><mo>∈</mo><mi>N</mi></math></span>. The general theory then tells us that there is a tube domain <span><math><mi>T</mi><mo>=</mo><mi>N</mi><mi>exp</mi><mo></mo><mo>(</mo><mi>i</mi><mi>Λ</mi><mo>)</mo><mo>⊂</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>C</mi></mrow></msub></math></span> such that each <span><math><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>a</mi></mrow></msub></math></span> extends to a holomorphic function on the scaled tube <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>a</mi></mrow></msub><mo>=</mo><mi>N</mi><mi>exp</mi><mo></mo><mo>(</mo><mi>i</mi><mi>Ad</mi><mo>(</mo><mi>a</mi><mo>)</mo><mi>Λ</mi><mo>)</mo></math></span>. We
我们关注的是非紧凑类型的黎曼对称空间 Z=G/K，更确切地说，是将∂Z 边界上的广义函数映射为 Z 上的λ特征函数的泊松变换 Pλ。我们特别强调了自然作用于 Z 和∂Z 的最大单能群 N<G。Z 上的 N 轨道由一个环 A=(R>0)r<G（岩泽）参数化，让水平 a∈A 在射线上趋向于 0，我们就可以通过 lima→0Na 在 ∂Z 中检索到作为开放密集轨道的 N（布鲁哈特）。对于正参数 λ，函数 f∈L2(N) 的泊松变换 Pλ 是定义的和注入的，我们从复分析的角度给出了 Pλ(L2(N))的新特征。为此，我们将特征函数 ϕ=Pλ(f) 视为 N 轨道上的函数族 (ja)a∈A，即 n∈N 时 ϕa(n)=j(na)。一般理论告诉我们，存在一个管域 T=Nexp(iΛ)⊂NC，使得每个 ϕa 在缩放管 Ta=Nexp(iAd(a)Λ) 上扩展为一个全形函数。我们定义了管子 T 上的一类 N 不变权函数 wλ，对每一个 a∈A 将它们重标度为 Ta 上的权 wλ,a，并证明每个 ja 位于 L2 加权伯格曼空间 B(Ta,wλ,a):=O(Ta)∩L2(Ta,wλ,a)。文章的主要结果将 Pλ(L2(N))描述为ϕa∈B(Ta,wλ,a)和‖ϕ‖：=supa∈AaReλ-2ρ‖ϕa‖Ba,λ<∞成立的特征函数。
{"title":"Poisson transform and unipotent complex geometry","authors":"Heiko Gimperlein , Bernhard Krötz , Luz Roncal , Sundaram Thangavelu","doi":"10.1016/j.jfa.2024.110742","DOIUrl":"10.1016/j.jfa.2024.110742","url":null,"abstract":"<div><div>Our concern is with Riemannian symmetric spaces <span><math><mi>Z</mi><mo>=</mo><mi>G</mi><mo>/</mo><mi>K</mi></math></span> of the non-compact type and more precisely with the Poisson transform <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>λ</mi></mrow></msub></math></span> which maps generalized functions on the boundary ∂<em>Z</em> to <em>λ</em>-eigenfunctions on <em>Z</em>. Special emphasis is given to a maximal unipotent group <span><math><mi>N</mi><mo><</mo><mi>G</mi></math></span> which naturally acts on both <em>Z</em> and ∂<em>Z</em>. The <em>N</em>-orbits on <em>Z</em> are parametrized by a torus <span><math><mi>A</mi><mo>=</mo><msup><mrow><mo>(</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>></mo><mn>0</mn></mrow></msub><mo>)</mo></mrow><mrow><mi>r</mi></mrow></msup><mo><</mo><mi>G</mi></math></span> (Iwasawa) and letting the level <span><math><mi>a</mi><mo>∈</mo><mi>A</mi></math></span> tend to 0 on a ray we retrieve <em>N</em> via <span><math><msub><mrow><mi>lim</mi></mrow><mrow><mi>a</mi><mo>→</mo><mn>0</mn></mrow></msub><mo></mo><mi>N</mi><mi>a</mi></math></span> as an open dense orbit in ∂<em>Z</em> (Bruhat). For positive parameters <em>λ</em> the Poisson transform <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>λ</mi></mrow></msub></math></span> is defined and injective for functions <span><math><mi>f</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>N</mi><mo>)</mo></math></span> and we give a novel characterization of <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>N</mi><mo>)</mo><mo>)</mo></math></span> in terms of complex analysis. For that we view eigenfunctions <span><math><mi>ϕ</mi><mo>=</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>(</mo><mi>f</mi><mo>)</mo></math></span> as families <span><math><msub><mrow><mo>(</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>a</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>a</mi><mo>∈</mo><mi>A</mi></mrow></msub></math></span> of functions on the <em>N</em>-orbits, i.e. <span><math><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>a</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mi>ϕ</mi><mo>(</mo><mi>n</mi><mi>a</mi><mo>)</mo></math></span> for <span><math><mi>n</mi><mo>∈</mo><mi>N</mi></math></span>. The general theory then tells us that there is a tube domain <span><math><mi>T</mi><mo>=</mo><mi>N</mi><mi>exp</mi><mo></mo><mo>(</mo><mi>i</mi><mi>Λ</mi><mo>)</mo><mo>⊂</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>C</mi></mrow></msub></math></span> such that each <span><math><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>a</mi></mrow></msub></math></span> extends to a holomorphic function on the scaled tube <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>a</mi></mrow></msub><mo>=</mo><mi>N</mi><mi>exp</mi><mo></mo><mo>(</mo><mi>i</mi><mi>Ad</mi><mo>(</mo><mi>a</mi><mo>)</mo><mi>Λ</mi><mo>)</mo></math></span>. We ","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 3","pages":"Article 110742"},"PeriodicalIF":1.7,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-06DOI: 10.1016/j.jfa.2024.110737
Xiumin Du, Jianhui Li
We obtain estimates of the maximal Schrödinger operator in using polynomial partitioning, bilinear refined Strichartz estimates, and weighted restriction estimates.
{"title":"Lp estimates of the maximal Schrödinger operator in Rn","authors":"Xiumin Du, Jianhui Li","doi":"10.1016/j.jfa.2024.110737","DOIUrl":"10.1016/j.jfa.2024.110737","url":null,"abstract":"<div><div>We obtain <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> estimates of the maximal Schrödinger operator in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> using polynomial partitioning, bilinear refined Strichartz estimates, and weighted restriction estimates.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 3","pages":"Article 110737"},"PeriodicalIF":1.7,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-06DOI: 10.1016/j.jfa.2024.110734
Liam Mazurowski
We show that a Weyl law holds for the variational spectrum of the p-Laplacian. More precisely, let be the variational spectrum of on a closed Riemannian manifold and let be the associated counting function. Then we have a Weyl law This confirms a conjecture of Friedlander. The proof is based on ideas of Gromov [5] and Liokumovich, Marques, Neves [7].
{"title":"A Weyl law for the p-Laplacian","authors":"Liam Mazurowski","doi":"10.1016/j.jfa.2024.110734","DOIUrl":"10.1016/j.jfa.2024.110734","url":null,"abstract":"<div><div>We show that a Weyl law holds for the variational spectrum of the <em>p</em>-Laplacian. More precisely, let <span><math><msubsup><mrow><mo>(</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></msubsup></math></span> be the variational spectrum of <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> on a closed Riemannian manifold <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>g</mi><mo>)</mo></math></span> and let <span><math><mi>N</mi><mo>(</mo><mi>λ</mi><mo>)</mo><mo>=</mo><mi>#</mi><mo>{</mo><mi>i</mi><mo>:</mo><mspace></mspace><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo><</mo><mi>λ</mi><mo>}</mo></math></span> be the associated counting function. Then we have a Weyl law<span><span><span><math><mi>N</mi><mo>(</mo><mi>λ</mi><mo>)</mo><mo>∼</mo><mi>c</mi><mi>vol</mi><mo>(</mo><mi>X</mi><mo>)</mo><msup><mrow><mi>λ</mi></mrow><mrow><mi>n</mi><mo>/</mo><mi>p</mi></mrow></msup><mo>.</mo></math></span></span></span> This confirms a conjecture of Friedlander. The proof is based on ideas of Gromov <span><span>[5]</span></span> and Liokumovich, Marques, Neves <span><span>[7]</span></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 3","pages":"Article 110734"},"PeriodicalIF":1.7,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-05DOI: 10.1016/j.jfa.2024.110738
Wontae Kim, Juha Kinnunen, Lauri Särkiö
We discuss a Lipschitz truncation technique for parabolic double-phase problems of p-Laplace type in order to prove energy estimates and uniqueness results for the Dirichlet problem. Moreover, we show existence for a non-homogeneous double-phase problem. The Lipschitz truncation method is based on a Whitney-type covering result and a related partition of unity in the intrinsic geometry for the double-phase problem.
{"title":"Lipschitz truncation method for parabolic double-phase systems and applications","authors":"Wontae Kim, Juha Kinnunen, Lauri Särkiö","doi":"10.1016/j.jfa.2024.110738","DOIUrl":"10.1016/j.jfa.2024.110738","url":null,"abstract":"<div><div>We discuss a Lipschitz truncation technique for parabolic double-phase problems of <em>p</em>-Laplace type in order to prove energy estimates and uniqueness results for the Dirichlet problem. Moreover, we show existence for a non-homogeneous double-phase problem. The Lipschitz truncation method is based on a Whitney-type covering result and a related partition of unity in the intrinsic geometry for the double-phase problem.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 3","pages":"Article 110738"},"PeriodicalIF":1.7,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-05DOI: 10.1016/j.jfa.2024.110732
Ryoya Arimoto
We prove that if a totally disconnected locally compact group admits a topologically free boundary, then the reduced crossed product of continuous functions on its Furstenberg boundary by the group is simple. We also prove a partial converse of this result.
{"title":"Simplicity of crossed products of the actions of totally disconnected locally compact groups on their boundaries","authors":"Ryoya Arimoto","doi":"10.1016/j.jfa.2024.110732","DOIUrl":"10.1016/j.jfa.2024.110732","url":null,"abstract":"<div><div>We prove that if a totally disconnected locally compact group admits a topologically free boundary, then the reduced crossed product of continuous functions on its Furstenberg boundary by the group is simple. We also prove a partial converse of this result.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 3","pages":"Article 110732"},"PeriodicalIF":1.7,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-30DOI: 10.1016/j.jfa.2024.110697
F. Nier , C. Gérard
{"title":"Corrigendum to “Mourre theory for analytically fibered operators” [J. Funct. Anal. 152 (1) (1998) 202–219]","authors":"F. Nier , C. Gérard","doi":"10.1016/j.jfa.2024.110697","DOIUrl":"10.1016/j.jfa.2024.110697","url":null,"abstract":"","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 3","pages":"Article 110697"},"PeriodicalIF":1.7,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142551914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-28DOI: 10.1016/j.jfa.2024.110723
Zhi Qi
In this paper, on the complex field , we prove two integral formulae for the Hankel–Mellin transform and the double Fourier–Mellin transform of Bessel functions, both resulting the hypergeometric function. As two applications, we use the former integral formula to make explicit the spectral formula of Bruggeman and Motohashi for the fourth moment of Dedekind zeta function over the Gaussian number field and to establish a spectral formula for the Hecke-eigenvalue twisted second moment of central L-values for the Picard group . Moreover, we develop the theory of distributional Hankel transform on .
本文在复数场 C 上证明了贝塞尔函数的汉克尔-梅林变换和双傅里叶-梅林变换的两个积分公式，这两个积分公式都产生了超几何函数。作为两个应用，我们利用前一个积分公式明确了布鲁格曼和本桥对高斯数域 Q(i) 的 Dedekind zeta 函数第四矩的谱公式，并建立了皮卡组 PGL2(Z[i]) 的赫克特征值扭转中心 L 值第二矩的谱公式。此外，我们还发展了 C∖{0} 上的分布汉克尔变换理论。
{"title":"On the Hankel transform of Bessel functions on complex numbers and explicit spectral formulae over the Gaussian field","authors":"Zhi Qi","doi":"10.1016/j.jfa.2024.110723","DOIUrl":"10.1016/j.jfa.2024.110723","url":null,"abstract":"<div><div>In this paper, on the complex field <span><math><mi>C</mi></math></span>, we prove two integral formulae for the Hankel–Mellin transform and the double Fourier–Mellin transform of Bessel functions, both resulting the hypergeometric function. As two applications, we use the former integral formula to make explicit the spectral formula of Bruggeman and Motohashi for the fourth moment of Dedekind zeta function over the Gaussian number field <span><math><mi>Q</mi><mo>(</mo><mi>i</mi><mo>)</mo></math></span> and to establish a spectral formula for the Hecke-eigenvalue twisted second moment of central <em>L</em>-values for the Picard group <span><math><msub><mrow><mi>PGL</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>Z</mi><mo>[</mo><mi>i</mi><mo>]</mo><mo>)</mo></math></span>. Moreover, we develop the theory of distributional Hankel transform on <span><math><mi>C</mi><mo>∖</mo><mo>{</mo><mn>0</mn><mo>}</mo></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 3","pages":"Article 110723"},"PeriodicalIF":1.7,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-24DOI: 10.1016/j.jfa.2024.110717
Stamatis Pouliasis
For a positive Borel measure μ in the unit disc, we examine which weighted Dirichlet spaces can be identified with de Branges-Rovnyak spaces , with equivalent norms. We prove a necessary condition for the equality and we explore its consequences. For Carleson measures μ, we give a necessary and sufficient condition for the equality , for a certain outer function related with the balayage of μ on the unit circle, and we provide examples of those spaces.
对于单位圆盘中的正伯勒量μ，我们研究了哪些加权德里赫特空间 Dμ 可以与具有等效规范的 de Branges-Rovnyak 空间 Hb 标识。我们证明了 Dμ=Hb 相等的必要条件，并探讨了其后果。对于卡莱森量μ，我们给出了Dμ=Hbμ相等的必要条件和充分条件，条件是与单位圆上μ的巴拉维相关的某个外函数bμ，我们还提供了这些空间的例子。
{"title":"Weighted Dirichlet spaces that are de Branges-Rovnyak spaces with equivalent norms","authors":"Stamatis Pouliasis","doi":"10.1016/j.jfa.2024.110717","DOIUrl":"10.1016/j.jfa.2024.110717","url":null,"abstract":"<div><div>For a positive Borel measure <em>μ</em> in the unit disc, we examine which weighted Dirichlet spaces <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>μ</mi></mrow></msub></math></span> can be identified with de Branges-Rovnyak spaces <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>b</mi></mrow></msub></math></span>, with equivalent norms. We prove a necessary condition for the equality <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>μ</mi></mrow></msub><mo>=</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>b</mi></mrow></msub></math></span> and we explore its consequences. For Carleson measures <em>μ</em>, we give a necessary and sufficient condition for the equality <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>μ</mi></mrow></msub><mo>=</mo><msub><mrow><mi>H</mi></mrow><mrow><msub><mrow><mi>b</mi></mrow><mrow><mi>μ</mi></mrow></msub></mrow></msub></math></span>, for a certain outer function <span><math><msub><mrow><mi>b</mi></mrow><mrow><mi>μ</mi></mrow></msub></math></span> related with the balayage of <em>μ</em> on the unit circle, and we provide examples of those spaces.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 3","pages":"Article 110717"},"PeriodicalIF":1.7,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142551911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-24DOI: 10.1016/j.jfa.2024.110713
Ioannis Anapolitanos , Marco Olivieri , Sylvain Zalczer
This article focuses on isomerizations of molecules, i.e. chemical reactions during which a molecule is transformed into another one with atoms in a different spatial configuration. We consider the special case in which the system breaks into two submolecules whose internal geometry is solid during the whole procedure. We prove, under some conditions, that the distance between the two submolecules stays bounded during the reaction. This paper extends [Anapolitanos-Lewin, 2020] in two directions. The first one is that we relax assumptions that the ground state eigenspaces of the submolecules have to fulfill. The second one is that we allow semirelativistic kinetic energy as well. We provide an asymptotic expansion of the interaction energy between two molecules, including multipolar interactions and the van der Waals attraction. In addition to this static result, we proceed to a quasistatic analysis to investigate the variation of the energy when the nuclei move.
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Pub Date : 2024-10-24DOI: 10.1016/j.jfa.2024.110720
Rafał Latała, Marta Strzelecka
<div><div>We prove that for every <span><math><mi>p</mi><mo>,</mo><mi>q</mi><mo>∈</mo><mo>[</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>]</mo></math></span> and every random matrix <span><math><mi>X</mi><mo>=</mo><msub><mrow><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>i</mi><mo>≤</mo><mi>m</mi><mo>,</mo><mi>j</mi><mo>≤</mo><mi>n</mi></mrow></msub></math></span> with iid centered entries satisfying the <em>α</em>-regularity assumption <span><math><msub><mrow><mo>‖</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>‖</mo></mrow><mrow><mn>2</mn><mi>ρ</mi></mrow></msub><mo>≤</mo><mi>α</mi><msub><mrow><mo>‖</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>‖</mo></mrow><mrow><mi>ρ</mi></mrow></msub></math></span> for every <span><math><mi>ρ</mi><mo>≥</mo><mn>1</mn></math></span>, the expectation of the operator norm of <em>X</em> from <span><math><msubsup><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> to <span><math><msubsup><mrow><mi>ℓ</mi></mrow><mrow><mi>q</mi></mrow><mrow><mi>m</mi></mrow></msubsup></math></span> is comparable, up to a constant depending only on <em>α</em>, to<span><span><span><math><msup><mrow><mi>m</mi></mrow><mrow><mn>1</mn><mo>/</mo><mi>q</mi></mrow></msup><munder><mi>sup</mi><mrow><mi>t</mi><mo>∈</mo><msubsup><mrow><mi>B</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msubsup></mrow></munder><mo></mo><msub><mrow><mo>‖</mo><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></munderover><msub><mrow><mi>t</mi></mrow><mrow><mi>j</mi></mrow></msub><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>j</mi></mrow></msub><mo>‖</mo></mrow><mrow><mi>q</mi><mo>∧</mo><mi>Log</mi><mspace></mspace><mi>m</mi></mrow></msub><mo>+</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>1</mn><mo>/</mo><msup><mrow><mi>p</mi></mrow><mrow><mo>⁎</mo></mrow></msup></mrow></msup><munder><mi>sup</mi><mrow><mi>s</mi><mo>∈</mo><msubsup><mrow><mi>B</mi></mrow><mrow><msup><mrow><mi>q</mi></mrow><mrow><mo>⁎</mo></mrow></msup></mrow><mrow><mi>m</mi></mrow></msubsup></mrow></munder><mo></mo><msub><mrow><mo>‖</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>m</mi></mrow></munderover><msub><mrow><mi>s</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>‖</mo></mrow><mrow><msup><mrow><mi>p</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>∧</mo><mi>Log</mi><mspace></mspace><mi>n</mi></mrow></msub><mo>.</mo></math></span></span></span> We give more explicit formulas, expressed as exact functions of <em>p</em>, <em>q</em>, <em>m</em>, and <em>n</em>, for the two-sided bounds of the operator norms in the case when the entries <span><math><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub></math></span> are: Gaussia
{"title":"Operator ℓp → ℓq norms of random matrices with iid entries","authors":"Rafał Latała, Marta Strzelecka","doi":"10.1016/j.jfa.2024.110720","DOIUrl":"10.1016/j.jfa.2024.110720","url":null,"abstract":"<div><div>We prove that for every <span><math><mi>p</mi><mo>,</mo><mi>q</mi><mo>∈</mo><mo>[</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>]</mo></math></span> and every random matrix <span><math><mi>X</mi><mo>=</mo><msub><mrow><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>i</mi><mo>≤</mo><mi>m</mi><mo>,</mo><mi>j</mi><mo>≤</mo><mi>n</mi></mrow></msub></math></span> with iid centered entries satisfying the <em>α</em>-regularity assumption <span><math><msub><mrow><mo>‖</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>‖</mo></mrow><mrow><mn>2</mn><mi>ρ</mi></mrow></msub><mo>≤</mo><mi>α</mi><msub><mrow><mo>‖</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>‖</mo></mrow><mrow><mi>ρ</mi></mrow></msub></math></span> for every <span><math><mi>ρ</mi><mo>≥</mo><mn>1</mn></math></span>, the expectation of the operator norm of <em>X</em> from <span><math><msubsup><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> to <span><math><msubsup><mrow><mi>ℓ</mi></mrow><mrow><mi>q</mi></mrow><mrow><mi>m</mi></mrow></msubsup></math></span> is comparable, up to a constant depending only on <em>α</em>, to<span><span><span><math><msup><mrow><mi>m</mi></mrow><mrow><mn>1</mn><mo>/</mo><mi>q</mi></mrow></msup><munder><mi>sup</mi><mrow><mi>t</mi><mo>∈</mo><msubsup><mrow><mi>B</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msubsup></mrow></munder><mo></mo><msub><mrow><mo>‖</mo><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></munderover><msub><mrow><mi>t</mi></mrow><mrow><mi>j</mi></mrow></msub><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>j</mi></mrow></msub><mo>‖</mo></mrow><mrow><mi>q</mi><mo>∧</mo><mi>Log</mi><mspace></mspace><mi>m</mi></mrow></msub><mo>+</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>1</mn><mo>/</mo><msup><mrow><mi>p</mi></mrow><mrow><mo>⁎</mo></mrow></msup></mrow></msup><munder><mi>sup</mi><mrow><mi>s</mi><mo>∈</mo><msubsup><mrow><mi>B</mi></mrow><mrow><msup><mrow><mi>q</mi></mrow><mrow><mo>⁎</mo></mrow></msup></mrow><mrow><mi>m</mi></mrow></msubsup></mrow></munder><mo></mo><msub><mrow><mo>‖</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>m</mi></mrow></munderover><msub><mrow><mi>s</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>‖</mo></mrow><mrow><msup><mrow><mi>p</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>∧</mo><mi>Log</mi><mspace></mspace><mi>n</mi></mrow></msub><mo>.</mo></math></span></span></span> We give more explicit formulas, expressed as exact functions of <em>p</em>, <em>q</em>, <em>m</em>, and <em>n</em>, for the two-sided bounds of the operator norms in the case when the entries <span><math><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub></math></span> are: Gaussia","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 3","pages":"Article 110720"},"PeriodicalIF":1.7,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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