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Heat expansion and zeta 热膨胀和 zeta
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-05-23 DOI: 10.1007/s43034-024-00358-5
Alain Connes
{"title":"Heat expansion and zeta","authors":"Alain Connes","doi":"10.1007/s43034-024-00358-5","DOIUrl":"10.1007/s43034-024-00358-5","url":null,"abstract":"<div><p>We compute the full asymptotic expansion of the heat kernel <span>(textrm{Tr}(exp (-tD^2)))</span> where <i>D</i> is, assuming RH, the self-adjoint operator whose spectrum is formed of the imaginary parts of non-trivial zeros of the Riemann zeta function. The coefficients of the expansion are explicit expressions involving Bernoulli and Euler numbers. We relate the divergent terms with the heat kernel expansion of the Dirac square root of the prolate wave operator investigated in our joint work with Henri Moscovici.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151365","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}
引用次数: 0
The lateral order on Köthe–Bochner spaces and orthogonally additive operators 科特-波赫纳空间的侧序和正交相加算子
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-05-23 DOI: 10.1007/s43034-024-00360-x
Marat Pliev, Nariman Abasov, Nonna Dzhusoeva
{"title":"The lateral order on Köthe–Bochner spaces and orthogonally additive operators","authors":"Marat Pliev,&nbsp;Nariman Abasov,&nbsp;Nonna Dzhusoeva","doi":"10.1007/s43034-024-00360-x","DOIUrl":"10.1007/s43034-024-00360-x","url":null,"abstract":"<div><p>In this paper, we introduce a new class of regular orthogonally additive operators defined on a lattice-normed space <span>((mathcal {X},E))</span> and taking values in a vector lattice <i>F</i>. We show that the vector space <span>(mathcal{O}mathcal{A}_r(mathcal {X},F))</span> of all regular orthogonally additive operators from a <i>d</i>-decomposable lattice-normed space <span>((mathcal {X},E))</span> to a Dedekind complete vector lattice <i>F</i> is a Dedekind complete vector lattice and the lattice operations can be calculated by the Riesz–Kantorovich formulas. We find necessary and sufficient conditions for an orthogonally additive operator <span>(T:mathcal {X}rightarrow F)</span> to be dominated and obtain a criterion of the positivity of a nonlinear superposition operator <span>(T_N:E(X)rightarrow E)</span> defined on Köthe–Bochner space <i>E</i>(<i>X</i>) and taking values in Köthe-*Banach space <i>E</i>. Finally, we state some open problems.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141166350","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}
引用次数: 0
Harmonic functions with traces in Q type spaces related to weights Q 型空间中与权重有关的迹的谐函数
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-05-17 DOI: 10.1007/s43034-024-00363-8
Shengwen Liu, Chen Zhang, Pengtao Li
{"title":"Harmonic functions with traces in Q type spaces related to weights","authors":"Shengwen Liu,&nbsp;Chen Zhang,&nbsp;Pengtao Li","doi":"10.1007/s43034-024-00363-8","DOIUrl":"10.1007/s43034-024-00363-8","url":null,"abstract":"<div><p>In this article, via a family of convolution operators <span>({phi _t}_{t&gt;0})</span>, we characterize the extensions of a class of <i>Q</i> type spaces <span>(Q^{p,q}_{K,lambda }(mathbb {R}^n))</span> related with weights <span>(K(cdot ))</span>. Unlike the classical <i>Q</i> type spaces which are related with power functions, a general weight function <span>(K(cdot ))</span> is short of homogeneity of the dilation, and is not variable-separable. Under several assumptions on the integrability of <span>(K(cdot ))</span>, we establish a Carleson type characterization of <span>(Q^{p,q}_{K,lambda }(mathbb {R}^n))</span>. We provide several applications. For the spatial dimension <span>(n=1)</span>, such an extension result indicates a boundary characterization of a class of analytic functions on <span>(mathbb R^{2}_{+})</span>. For the case <span>(nge 2)</span>, the family <span>({phi _t}_{t&gt;0})</span> can be seen as a generalization of the fundamental solutions to fractional heat equations, Caffarelli–Silvestre extensions and time-space fractional equations, respectively. Moreover, the boundedness of convolution operators on <span>(Q^{p,q}_{K,lambda }(mathbb {R}^n))</span> is also obtained, including convolution singular integral operators and fractional integral operators.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140965239","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}
引用次数: 0
Variants of 2-local maps on function algebras 函数代数上 2 局部映射的变体
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-05-15 DOI: 10.1007/s43034-024-00366-5
Liguang Wang, Xueyan Yang, Lei Li
{"title":"Variants of 2-local maps on function algebras","authors":"Liguang Wang,&nbsp;Xueyan Yang,&nbsp;Lei Li","doi":"10.1007/s43034-024-00366-5","DOIUrl":"10.1007/s43034-024-00366-5","url":null,"abstract":"<div><p>We study several variants of 2-local isometries (or algebra isomorphisms) on some function algebras, e.g., Lipschitz algebras, algebras of differential functions, algebras of absolutely continuous functions and algebras of continuous functions with bounded variation. A typical result is this: if <span>(phi )</span> is surjective map between function algebra mentioned above with the property that for any pair <i>f</i>, <i>g</i> there is an algebra isomorphism <span>(phi _{f,g})</span> such that <span>(phi (f)phi (g)=phi _{f,g}(fg))</span>, then <span>(phi )</span> can be written as a weighted composition operator.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140972933","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}
引用次数: 0
Generalized Cesàro operator acting on Hilbert spaces of analytic functions 作用于解析函数希尔伯特空间的广义塞萨罗算子
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-05-14 DOI: 10.1007/s43034-024-00365-6
Alejandro Mas, Noel Merchán, Elena de la Rosa
{"title":"Generalized Cesàro operator acting on Hilbert spaces of analytic functions","authors":"Alejandro Mas,&nbsp;Noel Merchán,&nbsp;Elena de la Rosa","doi":"10.1007/s43034-024-00365-6","DOIUrl":"10.1007/s43034-024-00365-6","url":null,"abstract":"<div><p>Let <span>(mathbb {D})</span> denote the unit disc in <span>(mathbb {C})</span>. We define the generalized Cesàro operator as follows: </p><div><div><span>$$begin{aligned} C_{omega }(f)(z)=int _0^1 f(tz)left( frac{1}{z}int _0^z B^{omega }_t(u),textrm{d}uright) ,omega (t)textrm{d}t, end{aligned}$$</span></div></div><p>where <span>({B^{omega }_zeta }_{zeta in mathbb {D}})</span> are the reproducing kernels of the Bergman space <span>(A^{2}_{omega })</span> induced by a radial weight <span>(omega )</span> in the unit disc <span>(mathbb {D})</span>. We study the action of the operator <span>(C_{omega })</span> on weighted Hardy spaces of analytic functions <span>(mathcal {H}_{gamma })</span>, <span>(gamma &gt;0)</span> and on general weighted Bergman spaces <span>(A^{2}_{mu })</span>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-024-00365-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dunford–Pettis type properties of locally convex spaces 局部凸空间的邓福德-佩提斯类型特性
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-05-09 DOI: 10.1007/s43034-024-00359-4
Saak Gabriyelyan
{"title":"Dunford–Pettis type properties of locally convex spaces","authors":"Saak Gabriyelyan","doi":"10.1007/s43034-024-00359-4","DOIUrl":"10.1007/s43034-024-00359-4","url":null,"abstract":"<div><p>In 1953, Grothendieck introduced and studied the Dunford–Pettis property (the <span>({textrm{DP}})</span> property) and the strict Dunford–Pettis property (the strict <span>({textrm{DP}})</span> property). The <span>({textrm{DP}})</span> property of order <span>(pin [1,infty ])</span> for Banach spaces was introduced by Castillo and Sanchez in 1993. Being motivated by these notions, for <span>(p,qin [1,infty ],)</span> we define the quasi-Dunford–Pettis property of order <i>p</i> (the quasi <span>({textrm{DP}}_p)</span> property) and the sequential Dunford–Pettis property of order (<i>p</i>, <i>q</i>) (the sequential <span>({textrm{DP}}_{(p,q)})</span> property). We show that a locally convex space (lcs) <i>E</i> has the <span>({textrm{DP}})</span> property if the space <i>E</i> endowed with the Grothendieck topology <span>(tau _{Sigma '})</span> has the weak Glicksberg property, and <i>E</i> has the quasi <span>({textrm{DP}}_p)</span> property if the space <span>((E,tau _{Sigma '}) )</span> has the <i>p</i>-Schur property. We also characterize lcs with the sequential <span>({textrm{DP}}_{(p,q)})</span> property. Some permanent properties and relationships between Dunford–Pettis type properties are studied. Numerous (counter)examples are given. In particular, we give the first example of an lcs with the strict <span>({textrm{DP}})</span> property but without the <span>({textrm{DP}})</span> property and show that the completion of even normed spaces with the <span>({textrm{DP}})</span> property may not have the <span>({textrm{DP}})</span> property.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925522","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}
引用次数: 0
Banach spaces of sequences arising from infinite matrices 由无限矩阵产生的序列的巴拿赫空间
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-05-08 DOI: 10.1007/s43034-024-00356-7
A. Bërdëllima, N. L. Braha
{"title":"Banach spaces of sequences arising from infinite matrices","authors":"A. Bërdëllima,&nbsp;N. L. Braha","doi":"10.1007/s43034-024-00356-7","DOIUrl":"10.1007/s43034-024-00356-7","url":null,"abstract":"<div><p>Given an infinite matrix <span>(M=(m_{nk}))</span>, we study a family of sequence spaces <span>(ell _M^p)</span> associated with it. When equipped with a suitable norm <span>(Vert cdot Vert _{M,p})</span>, we prove some basic properties of the Banach spaces of sequences <span>((ell _M^p,Vert cdot Vert _{M,p}))</span>. In particular, we show that such spaces are separable and strictly/uniformly convex for a considerably large class of infinite matrices <i>M</i> for all <span>(p&gt;1)</span>. A special attention is given to the identification of the dual space <span>((ell _M^p )^*)</span>. Building on the earlier works of Bennett and Jägers, we extend and apply some classical factorization results to the sequence spaces <span>(ell _M^p)</span>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925521","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}
引用次数: 0
Geometric properties for a class of deformed trace functions 一类变形痕量函数的几何特性
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-05-08 DOI: 10.1007/s43034-024-00353-w
Frank Hansen
{"title":"Geometric properties for a class of deformed trace functions","authors":"Frank Hansen","doi":"10.1007/s43034-024-00353-w","DOIUrl":"10.1007/s43034-024-00353-w","url":null,"abstract":"<div><p>We investigate the geometric properties for a class of trace functions expressed in terms of the deformed logarithmic and exponential functions. We extend earlier results of Epstein, Hiai, Carlen and Lieb.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-024-00353-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925309","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On conjugations concerning idempotents 关于幂函数的共轭
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-05-06 DOI: 10.1007/s43034-024-00354-9
Xiao-Ming Xu, Yi Yuan, Yuan Li, Yong Chen
{"title":"On conjugations concerning idempotents","authors":"Xiao-Ming Xu,&nbsp;Yi Yuan,&nbsp;Yuan Li,&nbsp;Yong Chen","doi":"10.1007/s43034-024-00354-9","DOIUrl":"10.1007/s43034-024-00354-9","url":null,"abstract":"<div><p>We introduce the <i>C</i>-decomposition property for reducible bounded linear operators on a Hilbert space, and prove that an arbitrary idempotent operator has the <i>C</i>-decomposition property with respect to a particular space decomposition, which is related to Halmos’ two projections theory. Using this, we obtain a general explicit description for all the conjugations <i>C</i> such that a given idempotent operator is a <i>C</i>-projection. We also present a characterization of the ranges of <i>C</i>-projections for any conjugation <i>C</i>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886018","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}
引用次数: 0
Estimates of discrete Riesz potentials on discrete weighted Lebesgue spaces 离散加权勒贝格空间上离散里兹势的估算
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-05-05 DOI: 10.1007/s43034-024-00357-6
Xuebing Hao, Baode Li, Shuai Yang
{"title":"Estimates of discrete Riesz potentials on discrete weighted Lebesgue spaces","authors":"Xuebing Hao,&nbsp;Baode Li,&nbsp;Shuai Yang","doi":"10.1007/s43034-024-00357-6","DOIUrl":"10.1007/s43034-024-00357-6","url":null,"abstract":"<div><p>Let <span>(0&lt;alpha &lt;1)</span>. We obtain necessary and sufficient conditions for the boundedness of the discrete fractional Hardy–Littlewood maximal operators <span>(mathcal {M}_alpha )</span> on discrete weighted Lebesgue spaces. From this and a discrete variant of the Whitney decomposition theorem, necessary and sufficient conditions for the boundedness of the discrete Riesz potentials <span>(I_alpha )</span> on discrete weighted Lebesgue spaces are discussed. As an application, the boundedness of <span>(I_alpha )</span> on discrete weighted Morrey spaces is further obtained.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886020","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}
引用次数: 0
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