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On a Slice Hyper-Meromorphic Bergman Space 关于片超同构伯格曼空间
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-03-26 DOI: 10.1007/s11785-024-01504-6
Sofia Boudrai, Aiad Elgourari, Allal Ghanmi
{"title":"On a Slice Hyper-Meromorphic Bergman Space","authors":"Sofia Boudrai, Aiad Elgourari, Allal Ghanmi","doi":"10.1007/s11785-024-01504-6","DOIUrl":"https://doi.org/10.1007/s11785-024-01504-6","url":null,"abstract":"<p>We intend to introduce and investigate a new functional space on the quaternionic unit ball of slice hyper-meromorphic functions with unique pole at the origin. Mainly, we provide a concrete characterization of their elements and give the closed explicit expression of the associated reproducing kernel function. Moreover, we show that they are isometrically isomorphic to the configuration space on the positive real half line by means of an integral transform of Bargmann type. The closed formulas for this transform are given in two special cases.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"52 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140297697","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
Quadratic Fock Space Calculus (II): Positivity of the Preservation Operator and Linear Independence of the Quadratic Exponential Vectors 二次 Fock 空间微积分 (II)：保存算子的正性与二次指数向量的线性独立性
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-03-26 DOI: 10.1007/s11785-024-01503-7
Omar Alzeley, Habib Rebei, Hafedh Rguigui
{"title":"Quadratic Fock Space Calculus (II): Positivity of the Preservation Operator and Linear Independence of the Quadratic Exponential Vectors","authors":"Omar Alzeley, Habib Rebei, Hafedh Rguigui","doi":"10.1007/s11785-024-01503-7","DOIUrl":"https://doi.org/10.1007/s11785-024-01503-7","url":null,"abstract":"<p>It have been proved in Accardi and Dhahri (J Math Phys 51:2, 2010) that the set of the exponential vectors <span>(Phi (g), ; gin {mathcal {K}}:=L^2({mathbb {R}}^d)cap L^{infty }({mathbb {R}}^d))</span> associated with different test functions <span>(g_iin {mathcal {K}})</span>, are linearly independents. Even this result is true, we present an alternative proof that is consistent with the results of this paper. In this paper, we start by a review of some results on the quadratic Fock space obtained in Accardi and Dhahri (J Math Phys 51:2, 2010) and Rebei (J Math Anal Appl 439(1): 135–153, 2016) , then we prove that the number operator is positive for non negative test function from which we deduce that the creation operator is injective. As application of the injectivity, we give an algebraic proof of the linear independence of the quadratic exponential vectors <span>(Phi (g))</span>.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"18 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140297696","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
Characterization of Dual Scalable Frames 双可扩展性帧的特性分析
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-03-25 DOI: 10.1007/s11785-024-01516-2
Behine Heydarpour, Ali Akbar Arefijamaal, Arash Ghaani Farashahi
{"title":"Characterization of Dual Scalable Frames","authors":"Behine Heydarpour, Ali Akbar Arefijamaal, Arash Ghaani Farashahi","doi":"10.1007/s11785-024-01516-2","DOIUrl":"https://doi.org/10.1007/s11785-024-01516-2","url":null,"abstract":"<p>Scalable frames in separable Hilbert spaces have been recently introduced by Kutyniok et al. to modify a general frame and to generate a Parseval frame by rescaling frame vectors. The main framework proposed in this paper is based on the redundancy of frame elements and is used as input for classification. This method leads to a complete characterization of scalable frames in <span>(mathbb {R}^{2})</span> and <span>(mathbb {R}^{3})</span>. In addition, we introduce all possible choices for the scale coefficients of a given scalable frame. Finally, we discuss the scalability of duals frames. We divide the set of all scalable dual frames of a given frame into two disjoint subsets, containing and not containing an orthogonal basis. In particular, we prove that both of them are non-empty.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"31 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140297522","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
Traces for Sturm–Liouville Operators on a Caterpillar Graph 卡特彼勒图上的 Sturm-Liouville 算子轨迹
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-03-25 DOI: 10.1007/s11785-024-01505-5
Feng Wang, Chuan-Fu Yang, Natalia P. Bondarenko
{"title":"Traces for Sturm–Liouville Operators on a Caterpillar Graph","authors":"Feng Wang, Chuan-Fu Yang, Natalia P. Bondarenko","doi":"10.1007/s11785-024-01505-5","DOIUrl":"https://doi.org/10.1007/s11785-024-01505-5","url":null,"abstract":"<p>In this work, we consider the spectral problems for the Sturm–Liouville operators on a caterpillar graph with the standard matching conditions in the internal vertices and the Neumann or the Dirichlet conditions in the boundary vertices. The regularized trace formulae of these operators are established by using the residue techniques of complex analysis.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"15 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140297445","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
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
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