Annals of Functional Analysis最新文献

筛选
英文 中文
Lattice Lipschitz operators on (C(K)-) spaces (C(K)-)空间上的晶格Lipschitz算子
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2025-04-21 DOI: 10.1007/s43034-025-00426-4
Roger Arnau, Jose M. Calabuig, Enrique A. Sánchez-Pérez
{"title":"Lattice Lipschitz operators on (C(K)-) spaces","authors":"Roger Arnau,&nbsp;Jose M. Calabuig,&nbsp;Enrique A. Sánchez-Pérez","doi":"10.1007/s43034-025-00426-4","DOIUrl":"10.1007/s43034-025-00426-4","url":null,"abstract":"<div><p>Given a Banach lattice <i>L</i>,  the space of lattice Lipschitz operators on <i>L</i> has been introduced as a natural Lipschitz generalization of the linear notions of diagonal operator and multiplication operator on Banach function lattices. It is a particular space of superposition operators on Banach lattices. Motivated by certain procedures in Reinforcement Learning based on McShane–Whitney extensions of Lipschitz maps, this class has proven to be useful also in the classical context of Mathematical Analysis. In this paper, we discuss the properties of such operators when defined on spaces of continuous functions, focusing attention on the functional bounds for the pointwise Lipschitz inequalities defining the lattice Lipschitz operators, the representation theorems for these operators as vector-valued functions, and the corresponding dual spaces. Finally, and with possible applications in Artificial Intelligence in mind, we provide a McShane–Whitney extension theorem for these operators.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-025-00426-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143852573","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
Quadratic programming with one quadratic constraint in Hilbert spaces 希尔伯特空间中单二次约束的二次规划
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2025-04-15 DOI: 10.1007/s43034-025-00422-8
Santiago Gonzalez Zerbo, Alejandra Maestripieri, Francisco Martínez Pería
{"title":"Quadratic programming with one quadratic constraint in Hilbert spaces","authors":"Santiago Gonzalez Zerbo,&nbsp;Alejandra Maestripieri,&nbsp;Francisco Martínez Pería","doi":"10.1007/s43034-025-00422-8","DOIUrl":"10.1007/s43034-025-00422-8","url":null,"abstract":"<div><p>A quadratically constrained quadratic programming problem is considered in a Hilbert space setting, where neither the objective nor the constraint are convex functions. Necessary and sufficient conditions are provided to guarantee that the problem admits solutions for every initial data (in an adequate set).</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143830800","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
Flat extension technique for moment matrices of positive linear functionals over mixed polynomials and an application in quantum information 混合多项式正线性函数矩阵的平延伸技术及其在量子信息中的应用
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2025-04-09 DOI: 10.1007/s43034-025-00419-3
Thanh Hieu Le, Minh Toan Ho
{"title":"Flat extension technique for moment matrices of positive linear functionals over mixed polynomials and an application in quantum information","authors":"Thanh Hieu Le,&nbsp;Minh Toan Ho","doi":"10.1007/s43034-025-00419-3","DOIUrl":"10.1007/s43034-025-00419-3","url":null,"abstract":"<div><p>A <i>mixed polynomial</i>, or a <i>Hermitian polynomial</i>, is a (multivariate) complex polynomial with monomials in complex variables and their conjugates. This paper deals with two types of mixed polynomials: sums of squared magnitudes of mixed polynomials (SOS polynomials for short) and those of usual complex polynomials (shortly, SQN polynomials). It is obvious that SQN polynomials are SOS, but generally, the converse is invalid. Both SOS and SQN polynomials are always mixed ones. This paper aims to provide sufficient and necessary conditions for a mixed polynomial to be SOS or SQN via moment matrices and the polynomial degree. We then give a sufficient condition for a SOS polynomial to be SQN, based on its degree. To this end, we apply the flat extension theory to the moment matrices of SOS and SQN polynomials and consider some optimization problems over positive linear functionals defined on the <span>(*)</span>-vector space of these two polynomial types. Consequently, we also give a degree characteristic of polynomials in the radical of the SQN set, which is one of the interesting problems posed by D’Angelo (Adv Math 226:4607–4637, 2011). An application in quantum information is also discussed: We introduce a class of quantum matrices whose degree-four SQN polynomials simultaneously satisfy the nonnegative, SQN and SOS properties.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809229","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
Existence of countably many p-k-convex solutions for p-k-Hessian equations and systems p-k-Hessian方程和系统的可数多个p-k-凸解的存在性
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2025-04-08 DOI: 10.1007/s43034-025-00424-6
Meiqiang Feng
{"title":"Existence of countably many p-k-convex solutions for p-k-Hessian equations and systems","authors":"Meiqiang Feng","doi":"10.1007/s43034-025-00424-6","DOIUrl":"10.1007/s43034-025-00424-6","url":null,"abstract":"<div><p>This paper analyzes, by employing topological approaches, the solvability of equations and systems involving <i>p</i>-<i>k</i>-Hessian operator. We first provide sufficient conditions for the existence of infinitely many <i>p</i>-<i>k</i>-convex solutions for a <i>p</i>-<i>k</i>-Hessian equation. Then we discuss the existence of infinitely many <i>p</i>-<i>k</i>-convex solutions for a <i>p</i>-<i>k</i>-Hessian system. We also study the existence of three infinite families of <i>p</i>-<i>k</i>-convex solutions for <i>p</i>-<i>k</i>-Hessian equations and systems. An example is presented to illustrate the applicability of our main results.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143793234","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
Local and global Dunkl–Morrey-type spaces 局部和全局dunkl - morrey型空间
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2025-04-08 DOI: 10.1007/s43034-025-00425-5
M. Shi, N. Zhao, Y. Liu
{"title":"Local and global Dunkl–Morrey-type spaces","authors":"M. Shi,&nbsp;N. Zhao,&nbsp;Y. Liu","doi":"10.1007/s43034-025-00425-5","DOIUrl":"10.1007/s43034-025-00425-5","url":null,"abstract":"<div><p>In this paper, we introduce (weak) local and global Dunkl–Morrey-type spaces and investigate some properties of these spaces, such as embedding theorem, pre-dual spaces and norm-equivalence relationships with Herz-type spaces. The necessary and sufficient conditions for the boundedness of Dunkl-fractional-type maximal operators on these spaces are obtained. Moreover, a characterization of the Hardy local Dunkl–Morrey-type space and a block decomposition of local Dunkl–Morrey type spaces are established.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143793233","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
Heat equations associated to harmonic oscillator with exponential nonlinearity 具有指数非线性的谐振子热方程
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2025-04-01 DOI: 10.1007/s43034-025-00420-w
Divyang G. Bhimani, Mohamed Majdoub, Ramesh Manna
{"title":"Heat equations associated to harmonic oscillator with exponential nonlinearity","authors":"Divyang G. Bhimani,&nbsp;Mohamed Majdoub,&nbsp;Ramesh Manna","doi":"10.1007/s43034-025-00420-w","DOIUrl":"10.1007/s43034-025-00420-w","url":null,"abstract":"<div><p>We investigate the Cauchy problem for a heat equation involving a fractional harmonic oscillator and an exponential nonlinearity: </p><div><div><span>$$begin{aligned} partial _tu + (-Delta +varrho |x|^2)^{beta }u=f(u), quad (x,t)in {mathbb {R}}^dtimes (0,infty ), end{aligned}$$</span></div></div><p>where <span>(varrho ge 0,~beta &gt;0)</span> and <span>(f:{mathbb {R}}rightarrow {mathbb {R}})</span> exhibits exponential growth at infinity, with <span>(f(0)=0.)</span> We establish local well-posedness within the appropriate Orlicz spaces. Through the examination of small initial data in suitable Orlicz spaces, we obtain the existence of global weak-mild solutions. Additionally, precise decay estimates are presented for large time, indicating that the decay rate is influenced by the nonlinearity’s behavior near the origin. Moreover, we highlight that the existence of local nonnegative classical solutions is no longer guaranteed when certain nonnegative initial data are considered within the appropriate Orlicz space.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143740679","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
Projective joint spectra and reducing subspace of operator tuples 算子元组的射影联合谱与约简子空间
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2025-03-13 DOI: 10.1007/s43034-025-00417-5
Michael I. Stessin
{"title":"Projective joint spectra and reducing subspace of operator tuples","authors":"Michael I. Stessin","doi":"10.1007/s43034-025-00417-5","DOIUrl":"10.1007/s43034-025-00417-5","url":null,"abstract":"<div><p>If a tuple of bounded operators have a common reducing subspace of finite dimension, its projective joint spectrum has an algebraic component. In general, the converse is not true and there might be algebraic components in the projective joint spectrum without corresponding common reducing subspaces. In this paper, we give necessary and sufficient conditions for the occurrence of such correspondence.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143612003","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
Stochastic bundles, new classes of Gaussian processes and white noise-space analysis indexed by measures 随机束,高斯过程的新类别和白噪声空间分析索引的措施
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2025-03-10 DOI: 10.1007/s43034-025-00416-6
Daniel Alpay, Palle Jorgensen
{"title":"Stochastic bundles, new classes of Gaussian processes and white noise-space analysis indexed by measures","authors":"Daniel Alpay,&nbsp;Palle Jorgensen","doi":"10.1007/s43034-025-00416-6","DOIUrl":"10.1007/s43034-025-00416-6","url":null,"abstract":"<div><p>Starting from a fixed measure space <span>((X, {mathcal {F}}, mu ))</span>, with <span>(mu )</span> a positive sigma-finite measure defined on the sigma-algebra <span>({mathcal {F}})</span>, we continue here our study of a generalization <span>(W^{(mu )})</span> of Brownian motion, and introduce a corresponding white-noise process. In detail, the generalized Brownian motion is a centered Gaussian process <span>(W^{(mu )})</span>, indexed by the elements <i>A</i> in <span>({mathcal {F}})</span> of finite <span>(mu )</span> measure, and with covariance function <span>(mu (Acap B))</span>. The purpose of our present paper is to make precise and study the corresponding white-noise process, i.e., a point-wise process which is indexed by <i>X</i>, and which arises as a generalized <span>(mu )</span> derivative of <span>(W^{(mu )})</span>. A key tool in our definition and analysis of this pair is a construction of three operators between the underlying Hilbert spaces. One of these operators is a stochastic integral, the second is a gradient associated with the measure <span>(mu )</span>, and the third is a mathematical expectation in the underlying probability space. We show that, with the setting of families of processes indexed by sets of measures <span>(mu )</span>, our results lead to new stochastic bundles. They serve in turn to extend the tool set for stochastic calculus.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-025-00416-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143581185","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 some local geometry of Orlicz sequence spaces equipped with the p-Amemiya norm 具有p-Amemiya范数的Orlicz序列空间的某些局部几何
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2025-03-03 DOI: 10.1007/s43034-025-00415-7
Xiaoyan Li, Yunan Cui
{"title":"On some local geometry of Orlicz sequence spaces equipped with the p-Amemiya norm","authors":"Xiaoyan Li,&nbsp;Yunan Cui","doi":"10.1007/s43034-025-00415-7","DOIUrl":"10.1007/s43034-025-00415-7","url":null,"abstract":"<div><p>In this paper, criteria for strong U-points and H-property in Orlicz sequence spaces equipped with the <i>p</i>-Amemiya norm <span>((1&lt; p&lt;infty ))</span> are given. Next, compactly locally uniform rotundity and locally uniform rotundity of these spaces are deduced. Obtained results broaden the knowledge about these notions in Orlicz sequence spaces equipped with the <i>p</i>-Amemiya norm.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143533168","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
Smoothness and approximate smoothness in normed linear spaces and operator spaces 赋范线性空间和算子空间中的光滑性和近似光滑性
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2025-02-28 DOI: 10.1007/s43034-025-00413-9
Jacek Chmieliński, Souvik Ghosh, Kallol Paul, Debmalya Sain
{"title":"Smoothness and approximate smoothness in normed linear spaces and operator spaces","authors":"Jacek Chmieliński,&nbsp;Souvik Ghosh,&nbsp;Kallol Paul,&nbsp;Debmalya Sain","doi":"10.1007/s43034-025-00413-9","DOIUrl":"10.1007/s43034-025-00413-9","url":null,"abstract":"<div><p>The paper is devoted to studies on exact and approximate smoothness in normed linear spaces. In particular, we develop the concept of approximate smoothness and present some of its new properties and characterizations. We pay a special attention to spaces of linear bounded operators on Banach and Hilbert spaces.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513433","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
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信