Advances in Operator Theory最新文献_第4页

Residual-weighted decomposition of positive operators 正算子的残差加权分解

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Advances in Operator Theory Pub Date : 2026-05-29 DOI: 10.1007/s43036-026-00509-6

James Tian

{"title":"Residual-weighted decomposition of positive operators","authors":"James Tian","doi":"10.1007/s43036-026-00509-6","DOIUrl":"10.1007/s43036-026-00509-6","url":null,"abstract":"<div>This paper investigates an iterative rank-one decomposition scheme for positive operators on a Hilbert space based on a residual-weighted congruence update. At each step the operator is compressed along a chosen unit vector while remaining inside the positive cone, and the resulting map defines a monotone dynamical system on the cone of positive operators. We prove that the associated residuals admit a canonical telescoping decomposition into rank-one terms and a limiting positive operator, and we identify this limit together with an exact energy identity expressing the defect between the initial and limiting operators as a convergent series of rank-one contributions. In the case where the iteration exhausts the operator, the residual directions form a Parseval frame for the natural range space, yielding a constructive procedure that produces Parseval frames without spectral calculus. We further solve the inverse problem by characterizing those decreasing chains with rank-one steps that arise from such dynamics via an intrinsic normalization condition involving the Moore–Penrose inverse. For trace-class operators we obtain a scalar energy identity and show that mild greedy or density conditions on the chosen directions guarantee exhaustion. An application to reproducing kernel Hilbert spaces illustrates the abstract results.</div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148173337","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

Affine AP-frames and stationary random processes 仿射ap帧与平稳随机过程

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Advances in Operator Theory Pub Date : 2026-05-29 DOI: 10.1007/s43036-026-00514-9

Hernán D. Centeno, Juan M. Medina

引用次数: 0

K-positivity preserver of matrix polynomials 矩阵多项式的k -正守恒

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Advances in Operator Theory Pub Date : 2026-05-29 DOI: 10.1007/s43036-026-00512-x

Philipp J. di Dio, Lars-Luca Langer

{"title":"K-positivity preserver of matrix polynomials","authors":"Philipp J. di Dio, Lars-Luca Langer","doi":"10.1007/s43036-026-00512-x","DOIUrl":"10.1007/s43036-026-00512-x","url":null,"abstract":"<div>For any closed (Ksubseteq mathbb {R}^n), recently all K-positivity preserver have been characterized, i.e., all linear operators (T:mathbb {R}[x_1,dots ,x_n]rightarrow mathbb {R}[x_1,dots ,x_n]) such that (Tpge 0) on K for all (pge 0) on K. An important extension of polynomials (mathbb {R}[x_1,dots ,x_n]) with real coefficients are polynomials (mathbb {R}^{mtimes m}[x_1,dots ,x_n]) with matrix coefficients. Non-negativity on K for matrix polynomials with Hermitian coefficients (textrm{Herm}_m) is then (p(x)succeq 0) for all (xin K). In the current work, we investigate linear operators (T:textrm{Herm}_m[x_1,dots ,x_n]rightarrow textrm{Herm}_m[x_1,dots ,x_n]). We focus on matrix K-positivity preserver, i.e., (Tpsucceq 0) on K for all (psucceq 0) on K. For (K=mathbb {R}^n) and compact sets (Ksubseteq mathbb {R}^n), we give characterizations of matrix K-positivity preservers. We discuss the difference between the real and the matrix coefficient case and where our proof fails for general sets (Ksubseteq mathbb {R}^n) with (Kne mathbb {R}^n) and K non-compact.</div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-026-00512-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148173336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fredholmness of singular integral operators with continuous coefficients on Banach function spaces over the real line 实线上Banach函数空间上连续系数奇异积分算子的收敛性

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Advances in Operator Theory Pub Date : 2026-05-25 DOI: 10.1007/s43036-026-00510-z

Márcio Valente

引用次数: 0

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

引用次数: 0

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

引用次数: 0