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Complex Analysis and Operator Theory最新文献

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The Jacobi Operator on $$(-1,1)$$ and Its Various m-Functions $$(-1,1)$$上的雅可比算子及其各种 m 函数
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-09-17 DOI: 10.1007/s11785-024-01576-4
Fritz Gesztesy, Lance L. Littlejohn, Mateusz Piorkowski, Jonathan Stanfill
{"title":"The Jacobi Operator on $$(-1,1)$$ and Its Various m-Functions","authors":"Fritz Gesztesy, Lance L. Littlejohn, Mateusz Piorkowski, Jonathan Stanfill","doi":"10.1007/s11785-024-01576-4","DOIUrl":"https://doi.org/10.1007/s11785-024-01576-4","url":null,"abstract":"<p>We offer a detailed treatment of spectral and Weyl–Titchmarsh–Kodaira theory for all self-adjoint Jacobi operator realizations of the differential expression </p><span>$$begin{aligned} tau _{alpha ,beta } =&amp;- (1-x)^{-alpha } (1+x)^{-beta }(d/dx) big ((1-x)^{alpha +1}(1+x)^{beta +1}big ) (d/dx), &amp;alpha , beta in {mathbb {R}}, , x in (-1,1), end{aligned}$$</span><p>in <span>(L^2big ((-1,1); (1-x)^{alpha } (1+x)^{beta } dxbig ))</span>, <span>(alpha , beta in {mathbb {R}})</span>. In addition to discussing the separated boundary conditions that lead to Jacobi orthogonal polynomials as eigenfunctions in detail, we exhaustively treat the case of coupled boundary conditions and illustrate the latter with the help of the general <span>(eta )</span>-periodic and Krein–von Neumann extensions. In particular, we treat all underlying Weyl–Titchmarsh–Kodaira and Green’s function induced <i>m</i>-functions and revisit their Nevanlinna–Herglotz property. We also consider connections to other differential operators associated with orthogonal polynomials such as Laguerre, Gegenbauer, and Chebyshev.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"34 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Powers of Regular Linear Relations 常规线性关系的幂
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-09-14 DOI: 10.1007/s11785-024-01593-3
Houcem Daoud
{"title":"The Powers of Regular Linear Relations","authors":"Houcem Daoud","doi":"10.1007/s11785-024-01593-3","DOIUrl":"https://doi.org/10.1007/s11785-024-01593-3","url":null,"abstract":"<p>In this paper, we analyse properties like nullity, defect, ascent and descent of the powers of regular linear relations. We improve some results related to closure and regularity of powers of linear relations in normed spaces. Further, the obtained results are applied to investigate the descent and essential descent spectrum and to give some stability results.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"12 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Entire Symmetric Operators in de Branges–Pontryagin Spaces and a Truncated Matrix Moment Problem 德布朗热-庞特里亚金空间中的全对称算子和截断矩阵矩问题
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-09-11 DOI: 10.1007/s11785-024-01591-5
Volodymyr Derkach, Harry Dym
{"title":"Entire Symmetric Operators in de Branges–Pontryagin Spaces and a Truncated Matrix Moment Problem","authors":"Volodymyr Derkach, Harry Dym","doi":"10.1007/s11785-024-01591-5","DOIUrl":"https://doi.org/10.1007/s11785-024-01591-5","url":null,"abstract":"<p>The role of de Branges–Pontryagin spaces as functional models for entire symmetric operators with finite equal deficiency indices and proper gauges in Pontryagin spaces is reviewed and then extended to symmetric operators that are not entire. These results are used to derive an operator representation for generalized Carathéodory functions. Enroute, boundary mappings and the characteristic function of <i>S</i> are defined. Generalized resolvents of symmetric operators <i>S</i> with non dense domains corresponding to single-valued representing extensions <span>({{widetilde{S}} })</span> are characterized in terms of the characteristic function of <i>S</i>. These results are applied to obtain a description of the set of solutions of an indefinite truncated matrix moment problem.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"5 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214592","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Orthogonal Polynomials Related to Arithmetic and Harmonic Sequences 论与算术序列和谐波序列有关的正交多项式
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-09-09 DOI: 10.1007/s11785-024-01589-z
Adhemar Bultheel, Andreas Lasarow
{"title":"On Orthogonal Polynomials Related to Arithmetic and Harmonic Sequences","authors":"Adhemar Bultheel, Andreas Lasarow","doi":"10.1007/s11785-024-01589-z","DOIUrl":"https://doi.org/10.1007/s11785-024-01589-z","url":null,"abstract":"<p>In this paper we study special systems of orthogonal polynomials on the unit circle. More precisely, with a view to the recurrence relations fulfilled by these orthogonal systems, we analyze a link of non-negative arithmetic to harmonic sequences as a main subject. Here, arithmetic sequences appear as coefficients of orthogonal polynomials and harmonic sequences as corresponding Szegő parameters.\u0000</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"274 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Jordan Curve Theorem on a 3D Ball Through Brownian Motion 三维球通过布朗运动的乔丹曲线定理
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-09-06 DOI: 10.1007/s11785-024-01595-1
Arni S. R. Srinivasa Rao, Steven G. Krantz
{"title":"A Jordan Curve Theorem on a 3D Ball Through Brownian Motion","authors":"Arni S. R. Srinivasa Rao, Steven G. Krantz","doi":"10.1007/s11785-024-01595-1","DOIUrl":"https://doi.org/10.1007/s11785-024-01595-1","url":null,"abstract":"<p>The Jordan curve theorem states that any simple closed curve in 3<i>D</i> space divides the space into two regions, an interior and an exterior. In this article, we prove the Jordan curve theorem on the boundary of a 3<i>D</i> ball that is inserted in a complex plane bundle. To do so, we make use of the Brownian motion principle, which is a continuous-time and continuous-state stochastic process. We begin by selecting a random point on an arbitrarily chosen complex plane within a bundle <i>G</i> and on the boundary of the 3D ball considered. Using the two-step random process developed on complex planes earlier by Srinivasa Rao (Multilevel contours on bundles of complex planes, 2022), we draw a contour from the initial point to the next point on this plane. We then continue this process until we finish the Jordan curve that connects points on the boundary of a ball within <i>G</i>.\u0000</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214594","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Essential Adjointness of Pseudo-Differential Operators on $$mathbb {Z}^n$$ 伪微分算子在 $$mathbb {Z}^n$$ 上的本质相邻性
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-09-05 DOI: 10.1007/s11785-024-01597-z
Ognjen Milatovic
{"title":"The Essential Adjointness of Pseudo-Differential Operators on $$mathbb {Z}^n$$","authors":"Ognjen Milatovic","doi":"10.1007/s11785-024-01597-z","DOIUrl":"https://doi.org/10.1007/s11785-024-01597-z","url":null,"abstract":"<p>In the setting of the lattice <span>(mathbb {Z}^n)</span> we consider a pseudo-differential operator <i>A</i> whose symbol belongs to a class defined on <span>(mathbb {Z}^ntimes mathbb {T}^n)</span>, where <span>(mathbb {T}^n)</span> is the <i>n</i>-torus. We realize <i>A</i> as an operator acting between the discrete Sobolev spaces <span>(H^{s_j}(mathbb {Z}^n))</span>, <span>(s_jin mathbb {R})</span>, <span>(j=1,2)</span>, with the discrete Schwartz space serving as the domain of <i>A</i>. We provide a sufficient condition for the essential adjointness of the pair <span>((A,,A^{dagger }))</span>, where <span>(A^{dagger })</span> is the formal adjoint of <i>A</i>.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"32 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Strong b-Suprametric Spaces and Fixed Point Principles 强 b 超空间和定点原理
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-09-04 DOI: 10.1007/s11785-024-01594-2
Maher Berzig
{"title":"Strong b-Suprametric Spaces and Fixed Point Principles","authors":"Maher Berzig","doi":"10.1007/s11785-024-01594-2","DOIUrl":"https://doi.org/10.1007/s11785-024-01594-2","url":null,"abstract":"<p>In this paper, we introduce the strong <i>b</i>-suprametric spaces in which we prove the fixed point principles of Banach and Edelstein. Moreover, we prove a variational principle of Ekeland and deduce a Caristi fixed point theorem. Furthermore, we introduce the strong <i>b</i>-supranormed linear spaces in which we establish the fixed point principles of Brouwer and Schauder. As applications, we study the existence of solutions to an integral equation and to a third-order boundary value problem.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Conditions Implying Self-adjointness and Normality of Operators 意味着算子自相接和规范性的条件
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-09-04 DOI: 10.1007/s11785-024-01596-0
Hranislav Stanković
{"title":"Conditions Implying Self-adjointness and Normality of Operators","authors":"Hranislav Stanković","doi":"10.1007/s11785-024-01596-0","DOIUrl":"https://doi.org/10.1007/s11785-024-01596-0","url":null,"abstract":"<p>In this paper, we give new characterizations of self-adjoint and normal operators on a Hilbert space <span>(mathcal {H})</span>. Among other results, we show that if <span>(mathcal {H})</span> is a finite-dimensional Hilbert space and <span>(Tin mathfrak {B}(mathcal {H}))</span>, then <i>T</i> is self-adjoint if and only if there exists <span>(p&gt;0)</span> such that <span>(|T|^ple |textrm{Re},(T)|^p)</span>. If in addition, <i>T</i> and <span>(textrm{Re},T)</span> are invertible, then <i>T</i> is self-adjoint if and only if <span>(log ,|T|le log ,|textrm{Re},(T)|)</span>. Considering the polar decomposition <span>(T=U|T|)</span> of <span>(Tin mathfrak {B}(mathcal {H}))</span>, we show that <i>T</i> is self-adjoint if and only if <i>T</i> is <i>p</i>-hyponormal (log-hyponormal) and <i>U</i> is self-adjoint. Also, if <span>(T=U|T|in mathfrak {B}({mathcal {H}}))</span> is a log-hyponormal operator and the spectrum of <i>U</i> is contained within the set of vertices of a regular polygon, then <i>T</i> is necessarily normal.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"37 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Rough Singular Integral Operators, Spherical Maximal Functions and Maximal Bochner-Riesz Operators on Grand Morrey Spaces 大莫里空间上的粗糙奇异积分算子、球面最大函数和最大波赫纳-里兹算子
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-09-02 DOI: 10.1007/s11785-024-01588-0
Kwok-Pun Ho
{"title":"Rough Singular Integral Operators, Spherical Maximal Functions and Maximal Bochner-Riesz Operators on Grand Morrey Spaces","authors":"Kwok-Pun Ho","doi":"10.1007/s11785-024-01588-0","DOIUrl":"https://doi.org/10.1007/s11785-024-01588-0","url":null,"abstract":"<p>This paper extends the Rubio de Francia extrapolation method to the grand Morrey spaces on Euclidean spaces. By using this extended extrapolation method, we obtain the boundedness of the rough singular integral operators, the spherical maximal functions and the maximal Bochner-Riesz operators on the grand Morrey spaces on Euclidean spaces.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"12 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Linear Recurrence of (Generalized) Hybrid Numbers Sequences and Moment Problems 论（广义）混合数列的线性递推和矩问题
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-08-31 DOI: 10.1007/s11785-024-01582-6
Abdallah Taia, Rajae Ben Taher, Bouazza El Wahbi
{"title":"On the Linear Recurrence of (Generalized) Hybrid Numbers Sequences and Moment Problems","authors":"Abdallah Taia, Rajae Ben Taher, Bouazza El Wahbi","doi":"10.1007/s11785-024-01582-6","DOIUrl":"https://doi.org/10.1007/s11785-024-01582-6","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Aim</h3><p>The aim of this study is to introduce definitions and explore properties of moment problems for sequences of generalized hybrid numbers satisfying a linear recursive equation.</p><h3 data-test=\"abstract-sub-heading\">Methods</h3><p>We analyze complex measures derived from the linear recurrence of hybrid numbers and generalized hybrid numbers sequences.</p><h3 data-test=\"abstract-sub-heading\">Results</h3><p>We present results pertaining to the moments of these complex measures.</p><h3 data-test=\"abstract-sub-heading\">Conclusions</h3><p>This study contributes to the understanding of moment problems in the context of generalized hybrid number sequences.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"2 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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