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Geometry of Five Point Sets in the Complex Ball 复杂球中五点集合的几何学
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-03-24 DOI: 10.1007/s11785-024-01502-8
Richard Rochberg
{"title":"Geometry of Five Point Sets in the Complex Ball","authors":"Richard Rochberg","doi":"10.1007/s11785-024-01502-8","DOIUrl":"https://doi.org/10.1007/s11785-024-01502-8","url":null,"abstract":"<p>We describe ten geometric functionals, four real and six complex, which determine the geometry of five point sets in the complex ball up to conformal automorphism. We give conditions on those parameters which are necessary and sufficient for there to be an associated five point set.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"294 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140204247","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
Estimation of Bounds for the Zeros of Polynomials and Regular Functions of a Quaternionic Variable 四元变量的多项式和正则函数的零点界限估计
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-03-23 DOI: 10.1007/s11785-024-01517-1
Abdullah Mir, Abrar Ahmad
{"title":"Estimation of Bounds for the Zeros of Polynomials and Regular Functions of a Quaternionic Variable","authors":"Abdullah Mir, Abrar Ahmad","doi":"10.1007/s11785-024-01517-1","DOIUrl":"https://doi.org/10.1007/s11785-024-01517-1","url":null,"abstract":"<p>The estimation of zeros of a polynomial with quaternionic coefficients has been done by many mathematicians in the recent past using various approaches. In this paper, we estimate the upper bounds for the zeros of polynomials and derive zero-free regions of some special regular functions of a quaternionic variable with restricted coefficients using the extended Schwarz’s lemma and the zero sets of a regular product. The obtained results for this subclass of polynomials and regular functions produce generalizations of a number of results known in the literature on this subject.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"294 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140204245","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
Several Properties of a Class of Generalized Harmonic Mappings 一类广义谐波映射的几个特性
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-03-23 DOI: 10.1007/s11785-024-01511-7
Bo-Yong Long, Qi-Han Wang
{"title":"Several Properties of a Class of Generalized Harmonic Mappings","authors":"Bo-Yong Long, Qi-Han Wang","doi":"10.1007/s11785-024-01511-7","DOIUrl":"https://doi.org/10.1007/s11785-024-01511-7","url":null,"abstract":"<p>We call the solution of a kind of second order homogeneous partial differential equation as real kernel <span>(alpha )</span>-harmonic mappings. In this paper, the representation theorem, the Lipschitz continuity, the univalency and the related problems of the real kernel <span>(alpha )</span>-harmonic mappings are explored.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"31 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140204584","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
Browder S-Resolvent Equation in Quaternionic Setting 四元背景下的布劳德 S-溶剂方程
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-03-22 DOI: 10.1007/s11785-024-01515-3
Hatem Baloudi, Aref Jeribi, Habib Zmouli
{"title":"Browder S-Resolvent Equation in Quaternionic Setting","authors":"Hatem Baloudi, Aref Jeribi, Habib Zmouli","doi":"10.1007/s11785-024-01515-3","DOIUrl":"https://doi.org/10.1007/s11785-024-01515-3","url":null,"abstract":"<p>This paper is devoted to the study of the <i>S</i>-eigenvalue of finite type of a bounded right quaternionic linear operator acting in a right quaternionic Hilbert space. The study is based on the different properties of the Riesz projection associated with the connected part of the <i>S</i>-spectrum. Furthermore, we introduce the left and right Browder <i>S</i>-resolvent operators. Inspired by the <i>S</i>-resolvent equation, we give the Browder’s <i>S</i>-resolvent equation in quaternionic setting.\u0000</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"17 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140204330","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
Minimal Invariant Subspaces for an Affine Composition Operator 仿射合成算子的最小不变子空间
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-03-18 DOI: 10.1007/s11785-024-01501-9
João R. Carmo, Ben Hur Eidt, S. Waleed Noor
{"title":"Minimal Invariant Subspaces for an Affine Composition Operator","authors":"João R. Carmo, Ben Hur Eidt, S. Waleed Noor","doi":"10.1007/s11785-024-01501-9","DOIUrl":"https://doi.org/10.1007/s11785-024-01501-9","url":null,"abstract":"<p>The composition operator <span>(C_{phi _a}f=fcirc phi _a)</span> on the Hardy–Hilbert space <span>(H^2({mathbb {D}}))</span> with affine symbol <span>(phi _a(z)=az+1-a)</span> and <span>(0&lt;a&lt;1)</span> has the property that the Invariant Subspace Problem for complex separable Hilbert spaces holds if and only if every minimal invariant subspace for <span>(C_{phi _a})</span> is one-dimensional. These minimal invariant subspaces are always singly-generated <span>( K_f:= overline{textrm{span} {f, C_{phi _a}f, C^2_{phi _a}f, ldots }})</span> for some <span>(fin H^2({mathbb {D}}))</span>. In this article we characterize the minimal <span>(K_f)</span> when <i>f</i> has a nonzero limit at the point 1 or if its derivative <span>(f')</span> is bounded near 1. We also consider the role of the zero set of <i>f</i> in determining <span>(K_f)</span>. Finally we prove a result linking universality in the sense of Rota with cyclicity.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"25 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140172652","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
Truncated Second Main Theorem for Holomorphic Curves on Annuli with Moving Hyperplanes 有移动超平面的环面上全形曲线的截断第二主定理
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-03-15 DOI: 10.1007/s11785-024-01500-w
Nhung Thi Nguyen, An Van Nguyen
{"title":"Truncated Second Main Theorem for Holomorphic Curves on Annuli with Moving Hyperplanes","authors":"Nhung Thi Nguyen, An Van Nguyen","doi":"10.1007/s11785-024-01500-w","DOIUrl":"https://doi.org/10.1007/s11785-024-01500-w","url":null,"abstract":"<p>In this paper, we establish some truncated second main theorems for holomorphic curve from an annulus into <span>({mathbb {P}}^n({mathbb {C}}))</span> and moving hyperplanes. We also use these results to solve unique problems with moving targets.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"2 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140147355","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
Hardy Type Theorems for Linear Canonical Dunkl Transform 线性典范邓克尔变换的哈代类型定理
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-03-13 DOI: 10.1007/s11785-023-01478-x
Ahmed Saoudi
{"title":"Hardy Type Theorems for Linear Canonical Dunkl Transform","authors":"Ahmed Saoudi","doi":"10.1007/s11785-023-01478-x","DOIUrl":"https://doi.org/10.1007/s11785-023-01478-x","url":null,"abstract":"<p>In this paper, we establish an analogue of Hardy’s theorems for the linear canonical Dunkl transform and fractional Dunkl transform, which generalizes a large class of a family of integral transforms. As application, we derive Hardy type theorems for fractional Hankel type transform, one dimension Dunkl Fresnel transform, linear canonical transform and fractional Fourier transform.\u0000</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"110 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140116989","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
Complex Symmetry of Linear Combinations of Composition Operators on the McCarthy–Bergman Space of Dirichlet Series 麦卡锡-伯格曼迪里希勒数列空间上合成算子线性组合的复对称性
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-03-12 DOI: 10.1007/s11785-024-01489-2
Cheng-shi Huang, Zhi-jie Jiang
{"title":"Complex Symmetry of Linear Combinations of Composition Operators on the McCarthy–Bergman Space of Dirichlet Series","authors":"Cheng-shi Huang, Zhi-jie Jiang","doi":"10.1007/s11785-024-01489-2","DOIUrl":"https://doi.org/10.1007/s11785-024-01489-2","url":null,"abstract":"<p>The complex symmetric linear combinations of composition operators on the McCarthy–Bergman spaces of Dirichlet series are completely characterized. The normality and self-adjointness of complex symmetric linear combinations of composition operators on such spaces are also characterized. Some images are given in order to find some interesting phenomena of <span>({mathcal {J}})</span>-symmetric such combinations.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"39 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140116986","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 Resolvent Matrix of the Truncated Hausdorff Matrix Moment Problem 论截断 Hausdorff 矩阵矩问题的残差矩阵
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-03-11 DOI: 10.1007/s11785-024-01499-0
{"title":"On the Resolvent Matrix of the Truncated Hausdorff Matrix Moment Problem","authors":"","doi":"10.1007/s11785-024-01499-0","DOIUrl":"https://doi.org/10.1007/s11785-024-01499-0","url":null,"abstract":"<h3>Abstract</h3> <p>We obtain the resolvent matrix of the truncated Hausdorff matrix moment (THMM) problem on the interval [<em>a</em>, <em>b</em>] in case of an even and odd number of moments expressed in terms of terminal point <em>b</em>. An explicit relation between the resolvent matrices of the THMM problem with respect to terminal points <em>a</em> and <em>b</em> is presented.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"39 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140117244","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 Decomposition for Pairs of Twisted Contractions 论成对扭曲收缩的分解
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-03-10 DOI: 10.1007/s11785-024-01497-2
{"title":"On Decomposition for Pairs of Twisted Contractions","authors":"","doi":"10.1007/s11785-024-01497-2","DOIUrl":"https://doi.org/10.1007/s11785-024-01497-2","url":null,"abstract":"<h3>Abstract</h3> <p>This paper presents Wold-type decomposition for various pairs of twisted contractions on Hilbert spaces. We achieve an explicit decomposition for pairs of twisted contractions such that the c.n.u. parts of the contractions are in <span> <span>(C_{00})</span> </span>. The structure for pairs of doubly twisted operators consisting of a power partial isometry has been discussed. It is also shown that for a pair <span> <span>((T,V^*))</span> </span> of twisted operators with <em>T</em> as a contraction and <em>V</em> as an isometry, there exists a unique (up to unitary equivalence) pair of doubly twisted isometries on the minimal isometric dilation space of <em>T</em>. Finally, we have given a characterization for pairs of doubly twisted isometries. </p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"33 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140099122","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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