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Stability of A(mathbb{T})-relations in (C^*)-algebras with tracial rank at most one 迹列最多为1的(C^*) -代数中A (mathbb{T}) -关系的稳定性
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2026-02-24 DOI: 10.1007/s10476-026-00139-3
J. Hua
{"title":"Stability of A(mathbb{T})-relations in (C^*)-algebras with tracial rank at most one","authors":"J. Hua","doi":"10.1007/s10476-026-00139-3","DOIUrl":"10.1007/s10476-026-00139-3","url":null,"abstract":"<div><p>An old and famous problem from the 1950s, popularized by Halmos, is that whether any pair of almost commuting contractive self-adjoint matrices are norm close to a pair of exactly commuting self-adjoint matrices? This question was solved affirmatively by Lin in the 1990's. In this paper, we study the general Halmos problem concerning unitary elements in <span>(C^*)</span>-algebras. Specifically, we first introduce the definition of A<span>(mathbb{T})</span>-relations, and then we give a necessary and sufficient condition for the stability of A<span>(mathbb{T})</span>-relations in any unital infinite\u0000dimensional simple separable <span>(C^*)</span>-algebra with tracial rank at most one. Finally, as applications, we show that many naturally occurring relations are A<span>(mathbb{T})</span>-relations, and thus the stability results of these relations can be obtained by applying the above conclusions.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"52 1","pages":"117 - 151"},"PeriodicalIF":0.5,"publicationDate":"2026-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147665677","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
Optimality conditions for change of variable operators in Sobolev spaces with mixed derivatives 具有混合导数的Sobolev空间中变量算子变化的最优性条件
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2026-02-23 DOI: 10.1007/s10476-026-00141-9
V. K. Nguyen
{"title":"Optimality conditions for change of variable operators in Sobolev spaces with mixed derivatives","authors":"V. K. Nguyen","doi":"10.1007/s10476-026-00141-9","DOIUrl":"10.1007/s10476-026-00141-9","url":null,"abstract":"<div><p>Change of variable plays an important role in constructing sparse grids for multivariate numerical integration of functions on \u0000<span>([0,1]^d)</span>. This is a modification of \u0000cubature formulae for functions supported in <span>([0,1]^d)</span> \u0000which yields the same order of convergence. \u0000In this paper we prove the necessary and sufficient conditions for the continuity of the change of variable operator in the Sobolev space with \u0000mixed derivatives <span>(boldsymbol{W}_p^m (mathbb{R}^d))</span>\u0000 with <span>(1leq p&lt;infty)</span>\u0000 . The result is then extended to the spaces on the unit cube \u0000 <span>(boldsymbol{W}_p^m([0,1]^d))</span>.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"52 1","pages":"291 - 306"},"PeriodicalIF":0.5,"publicationDate":"2026-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147665673","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
A note on the conjugates of nuclear operators 关于核算子共轭的注释
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2026-02-23 DOI: 10.1007/s10476-026-00142-8
M. Nowak
{"title":"A note on the conjugates of nuclear operators","authors":"M. Nowak","doi":"10.1007/s10476-026-00142-8","DOIUrl":"10.1007/s10476-026-00142-8","url":null,"abstract":"<div><p>Let <span>((Omega,Sigma,mu))</span> be a finite measure space and <i>X</i> and <i>Y</i> be real Banach spaces. It is shown that if <span>(T colon L^infty(mu,X)rightarrow Y)</span> is a <span>(sigma )</span>-order continuous\u0000operator and <span>(X ^{*} )</span> has the Radon-Nikodym property, <i>Y</i> is reflexive, then <i>T</i>\u0000is a nuclear operator if and only if its conjugate operator\u0000<span>(T ^{*} :Y ^{*} rightarrow L^1(mu,X ^{*} ))</span> is nuclear. In this case, <span>(|T| _{rm nuc}=|T ^{*} | _{rm nuc})</span>.\u0000</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"52 1","pages":"333 - 341"},"PeriodicalIF":0.5,"publicationDate":"2026-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147665737","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
Calderón–Zygmund operators and commutators on weighted Hardy spaces Calderón-Zygmund加权Hardy空间上的算子和换向子
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2026-02-23 DOI: 10.1007/s10476-026-00138-4
Y. Han, F. Liu, H. Wu
{"title":"Calderón–Zygmund operators and commutators on weighted Hardy spaces","authors":"Y. Han,&nbsp;F. Liu,&nbsp;H. Wu","doi":"10.1007/s10476-026-00138-4","DOIUrl":"10.1007/s10476-026-00138-4","url":null,"abstract":"<div><p>Two classes of Hörmander type conditions are introduced in the present paper. These conditions are weaker strictly than the classical standard Calderón–Zygmund kernels. A systematical study is given for the bounds of the Calderón–Zygmund operator with the above Hörmander type kernels and their commutators on the weighted Hardy spaces. The main results of this paper essentially improve a large classes of classical works. It should be pointed out that the main results are new, even in the unweighted case.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"52 1","pages":"87 - 115"},"PeriodicalIF":0.5,"publicationDate":"2026-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147665729","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
On the local regularity of the Hilbert transform 希尔伯特变换的局部正则性
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2026-01-26 DOI: 10.1007/s10476-025-00137-x
Y. Pan, J. Wang, Y. Yan
{"title":"On the local regularity of the Hilbert transform","authors":"Y. Pan,&nbsp;J. Wang,&nbsp;Y. Yan","doi":"10.1007/s10476-025-00137-x","DOIUrl":"10.1007/s10476-025-00137-x","url":null,"abstract":"<div><p>In this paper the local regularity of the Hilbert transform is studied, and local smoothness and real analyticity results are obtained.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"52 1","pages":"343 - 374"},"PeriodicalIF":0.5,"publicationDate":"2026-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-025-00137-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147665618","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
Bounds and asymptotic expansions for the radii of convexity and uniform convexity of normalized Bessel functions 归一化贝塞尔函数的凸半径和一致凸半径的界和渐近展开式
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2026-01-14 DOI: 10.1007/s10476-025-00136-y
Á. Baricz, P. Kumar, S. Singh
{"title":"Bounds and asymptotic expansions for the radii of convexity and uniform convexity of normalized Bessel functions","authors":"Á. Baricz,&nbsp;P. Kumar,&nbsp;S. Singh","doi":"10.1007/s10476-025-00136-y","DOIUrl":"10.1007/s10476-025-00136-y","url":null,"abstract":"<div><p>This paper explores the asymptotic behavior of the radii of convexity and uniform convexity for normalized Bessel functions with respect to large order. We provide detailed asymptotic expansions for these radii and establish recurrence relations for the associated coefficients. Additionally, we derive generalized bounds for the radii of convexity and uniform convexity by applying the Euler–Rayleigh inequality and potential polynomials. The asymptotic inversion method and Rayleigh sums are the main tools used in the proofs.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"52 1","pages":"1 - 43"},"PeriodicalIF":0.5,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147665736","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
Equality in Liakopoulos's generalized dual Loomis-Whitney inequality via Barthe's Reverse Brascamp-Lieb inequality 由Barthe的逆Brascamp-Lieb不等式证明Liakopoulos广义对偶Loomis-Whitney不等式中的等式
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2025-11-27 DOI: 10.1007/s10476-025-00134-0
K. J. Böröczky, F. Fodor, P. Kalantzopoulos
{"title":"Equality in Liakopoulos's generalized dual Loomis-Whitney inequality via Barthe's Reverse Brascamp-Lieb inequality","authors":"K. J. Böröczky,&nbsp;F. Fodor,&nbsp;P. Kalantzopoulos","doi":"10.1007/s10476-025-00134-0","DOIUrl":"10.1007/s10476-025-00134-0","url":null,"abstract":"<div><p>We use the characterization of the case of equality in Barthe's geometric reverse Brascamp-Lieb inequality to characterize equality in Liakopoulos's volume estimate in terms of sections by certain lower-dimensional linear subspaces.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 4","pages":"1229 - 1245"},"PeriodicalIF":0.5,"publicationDate":"2025-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145766276","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
Finely holomorphic functions in one and more complex variables-a survey 一个及多个复杂变量的精细全纯函数——综述
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2025-11-27 DOI: 10.1007/s10476-025-00135-z
M. El Kadiri
{"title":"Finely holomorphic functions in one and more complex variables-a survey","authors":"M. El Kadiri","doi":"10.1007/s10476-025-00135-z","DOIUrl":"10.1007/s10476-025-00135-z","url":null,"abstract":"<div><p>This paper is a survey on the theory of finely holomorphic\u0000functions in one variable as developed by Fuglede in the 1980s and\u0000in several variables as developed recently by El Kadiri, Fuglede and Wiegerinck. Some applications to pluripotential theory are also given.\u0000</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 4","pages":"1247 - 1266"},"PeriodicalIF":0.5,"publicationDate":"2025-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145766280","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
Normal operators in real and quaternionic Hilbert spaces 实数和四元Hilbert空间中的正规算子
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2025-11-24 DOI: 10.1007/s10476-025-00132-2
F.-H. Vasilescu
{"title":"Normal operators in real and quaternionic Hilbert spaces","authors":"F.-H. Vasilescu","doi":"10.1007/s10476-025-00132-2","DOIUrl":"10.1007/s10476-025-00132-2","url":null,"abstract":"<div><p>A new approach to normal operators in real Hilbert spaces is\u0000discussed, and a spectral representation is obtained, derived directly from the\u0000complex case. The results are then applied to quaternionic normal operators,\u0000regarded as a special class of real normal operators. This point of view allows us\u0000to consider their spectrum and associated measures to be defined on subsets of\u0000the complex plane, in a classical manner.\u0000</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 4","pages":"1455 - 1485"},"PeriodicalIF":0.5,"publicationDate":"2025-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145766244","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
Selected gems from the mathematics of Bent Fuglede - a centenary tribute 从Bent Fuglede的数学中精选的宝石-百年致敬
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2025-11-24 DOI: 10.1007/s10476-025-00124-2
C. Berg, K. Böröczky, M. El Kadiri, M. Kolountzakis, N. Zorii, L. Zsidó
{"title":"Selected gems from the mathematics of Bent Fuglede - a centenary tribute","authors":"C. Berg,&nbsp;K. Böröczky,&nbsp;M. El Kadiri,&nbsp;M. Kolountzakis,&nbsp;N. Zorii,&nbsp;L. Zsidó","doi":"10.1007/s10476-025-00124-2","DOIUrl":"10.1007/s10476-025-00124-2","url":null,"abstract":"","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 4","pages":"1117 - 1154"},"PeriodicalIF":0.5,"publicationDate":"2025-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145766278","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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