Advances in Operator Theory最新文献

Interpolating sequences for weighted spaces of analytic functions on Banach spaces Banach空间上解析函数加权空间的插值序列

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Advances in Operator Theory Pub Date : 2026-05-07 DOI: 10.1007/s43036-026-00505-w

Mario P. Maletzki

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Rapid decay for odometers 里程表的快速衰减

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Advances in Operator Theory Pub Date : 2026-05-05 DOI: 10.1007/s43036-026-00508-7

Slawomir Klimek, Matt McBride

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Infinitely many solutions for a class of fractional Kirchhoff problems with critical exponent 一类具有临界指数的分数阶Kirchhoff问题的无穷多解

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Advances in Operator Theory Pub Date : 2026-04-29 DOI: 10.1007/s43036-026-00506-9

M. R. Marcial, L. C. Paes-Leme, E. M. Martins, W. M. Ferreira

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On the idempotent operator and polar decomposition 幂等算子与极坐标分解

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Advances in Operator Theory Pub Date : 2026-04-13 DOI: 10.1007/s43036-025-00491-5

Chunyuan Deng, Xingxue Fu, Xiaohui Li

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Small representations associated with Heisenberg Gelfand pairs 与Heisenberg Gelfand对相关的小表示

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Advances in Operator Theory Pub Date : 2026-04-10 DOI: 10.1007/s43036-026-00504-x

Aymen Rahali, Sofien Hamdani

{"title":"Small representations associated with Heisenberg Gelfand pairs","authors":"Aymen Rahali, Sofien Hamdani","doi":"10.1007/s43036-026-00504-x","DOIUrl":"10.1007/s43036-026-00504-x","url":null,"abstract":"<div>Let ((K,H_V)) be a Heisenberg Gelfand pair and (G:=Kltimes H_V) be its associated semidirect product. Here, K is a compact Lie group acting smoothly on the Heisenberg group (H_V:=Vtimes mathbb {R},) where V is a finite-dimensional complex vector space. Let (widehat{G}) be the unitary dual of G equipped with the Fell topology. We say that (pi in widehat{G}) is a spherical representation of G if the restriction (pi |_K) of (pi ) to the subgroup K has a one-dimensional space of K-fixed vectors. Boidol, Ludwig and Müller have introduced the notion of the so-called small representations of G, that is all (pi in widehat{G}) that cannot be Hausdorff separated from the trivial one-dimensional representation (1_G) of G. Using a parametrization of the set of irreducible spherical representations due to work of Benson-Ratcliff, we show that any non-trivial spherical representation of G cannot be a small representation. Furthermore, we prove that the converse of this statement is false in the setting of the Heisenberg motion group (G_d:=U(d)ltimes H_{mathbb {C}^d}, din mathbb {N}^times .)</div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147642454","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Pullback attractors of non-autonomous nonclassical diffusion equations with state-dependent delay 具有状态相关延迟的非自治非经典扩散方程的回拉吸引子

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Advances in Operator Theory Pub Date : 2026-04-08 DOI: 10.1007/s43036-026-00498-6

Qiaozhen Ma, Tongtong Liang, Wenting Liu

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Frame dimension functions of g-frames g-框架的框架维函数

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Advances in Operator Theory Pub Date : 2026-04-07 DOI: 10.1007/s43036-026-00502-z

Tian Wang, Miao He

{"title":"Frame dimension functions of g-frames","authors":"Tian Wang, Miao He","doi":"10.1007/s43036-026-00502-z","DOIUrl":"10.1007/s43036-026-00502-z","url":null,"abstract":"<div>Frame theory has important applications in phase-retrieval problem, and the dimension function of a frame can serve as a candidate for measuring its phase retrievability. In this paper, we first investigate the relationship between phase retrievability and the dimension function of g-frames incorporating operator theory. We find that the dimension function of a phase-retrievable g-frame closely aligns with that of an ordinary frame. This consistency suggests that the dimension function of a g-frame can likewise act as a metric for measuring its phase retrieval capability. Specifically, we find that the exact PR-redundancy of a g-frame is equivalent to the exactness of its dimension function. The paper then investigates the structure of the dimension function range of g-frames. We find that, even when the number of operators in a g-frame is not less than n, significant differences remain from the case of ordinary frames regarding the structure of the dimension function range of g-Riesz basis and whether the range contains n. Finally, we present a method for examining the dimension function of a g-frame via its induced frame, along with a straightforward approach to construct g-frames whose dimension function range contains n.</div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147642412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The forward and backward shift on the Zygmund space of a tree 树的齐格蒙空间上的向前和向后移动

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Advances in Operator Theory Pub Date : 2026-03-30 DOI: 10.1007/s43036-026-00501-0

Itzama Delgadillo-García, Rubén A. Martínez-Avendaño

引用次数: 0

A complete asymptotic expansion for the semi-exponential Post–Widder operators 半指数后widder算子的完全渐近展开式

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Advances in Operator Theory Pub Date : 2026-03-24 DOI: 10.1007/s43036-026-00499-5

Ulrich Abel, Octavian Agratini, Radu Păltănea

引用次数: 0

Local symmetry and smoothness in the space of vector-valued continuous functions 向量值连续函数空间的局部对称性和光滑性