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On Recovering Dirac Operators with Two Delays 关于恢复有两个延迟的狄拉克算子
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-05-29 DOI: 10.1007/s11785-024-01543-z
Biljana Vojvodić, Nebojša Djurić, Vladimir Vladičić
{"title":"On Recovering Dirac Operators with Two Delays","authors":"Biljana Vojvodić, Nebojša Djurić, Vladimir Vladičić","doi":"10.1007/s11785-024-01543-z","DOIUrl":"https://doi.org/10.1007/s11785-024-01543-z","url":null,"abstract":"<p>We study the inverse spectral problems of recovering Dirac-type functional-differential operator with two constant delays <span>(a_1)</span> and <span>(a_2)</span> not less than one-third of the length the interval. It has been proved that the operator can be recovered uniquely from four spectra when <span>(2a_1+frac{a_2}{2})</span> is not less than the length of the interval, while it is not possible otherwise.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"237 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141190985","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
Clark Measures on Polydiscs Associated to Product Functions and Multiplicative Embeddings 与积函数和乘法嵌入相关的多圆盘上的克拉克量纲
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-05-21 DOI: 10.1007/s11785-024-01547-9
Nell P. Jacobsson
{"title":"Clark Measures on Polydiscs Associated to Product Functions and Multiplicative Embeddings","authors":"Nell P. Jacobsson","doi":"10.1007/s11785-024-01547-9","DOIUrl":"https://doi.org/10.1007/s11785-024-01547-9","url":null,"abstract":"<p>We study Clark measures on the unit polydisc, giving an overview of recent research and investigating the Clark measures of some new examples of multivariate inner functions. In particular, we study the relationship between Clark measures and multiplication; first by introducing compositions of inner functions and multiplicative embeddings, and then by studying products of one-variable inner functions.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"57 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141150145","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
Rate of Convergence for Double Rational Fourier Series 双有理傅里叶级数的收敛率
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-05-18 DOI: 10.1007/s11785-023-01479-w
Hardeepbhai J. Khachar, Rajendra G. Vyas
{"title":"Rate of Convergence for Double Rational Fourier Series","authors":"Hardeepbhai J. Khachar, Rajendra G. Vyas","doi":"10.1007/s11785-023-01479-w","DOIUrl":"https://doi.org/10.1007/s11785-023-01479-w","url":null,"abstract":"<p>We calculate the rate of convergence of the double rational Fourier series for regular, bounded, measurable, and two-variable functions. The rectangular oscillation of the two-variable function is used to quantify this rate. Additionally, we give an approximation of convergence rate of the double rational Fourier series for continuous functions with generalized bounded variation.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"50 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141059352","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
Semicommutators of Truncated Toeplitz Operators 截断托普利兹算子的半互调器
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-05-13 DOI: 10.1007/s11785-024-01540-2
Xi Zhao, Tao Yu
{"title":"Semicommutators of Truncated Toeplitz Operators","authors":"Xi Zhao, Tao Yu","doi":"10.1007/s11785-024-01540-2","DOIUrl":"https://doi.org/10.1007/s11785-024-01540-2","url":null,"abstract":"<p>In this paper semicommutators of truncated Toeplitz operators on some model space are discussed. We investigate when the product or the semicommutator of two truncated Toeplitz operators is zero, respectively. We also obtain a necessary and sufficient condition for the semicommutator of two truncated Toeplitz operators to be compact.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"191 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140939101","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
Regularity of the Berezin Transform on the Elementary Reinhardt Domains 基本莱因哈特域上的贝雷津变换正则性
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-05-13 DOI: 10.1007/s11785-024-01538-w
Linhe Yang, Qingyang Zou
{"title":"Regularity of the Berezin Transform on the Elementary Reinhardt Domains","authors":"Linhe Yang, Qingyang Zou","doi":"10.1007/s11785-024-01538-w","DOIUrl":"https://doi.org/10.1007/s11785-024-01538-w","url":null,"abstract":"<p>In this paper, we consider a class of logarithmically convex domains in <span>({mathbb {C}}^n)</span>, called elementary Reinhardt domains, which can be regarded as a natural generalization of Hartogs triangles. The purpose of this paper is twofold. On one hand, we will compute the explicit forms of the Bergman kernel of weighted Hilbert space with radial symbols. On the other hand, by using the expressions of the weighted Bergman kernel, we will show the regularity of the Berezin transform on the elementary Reinhardt domains.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"8 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140926615","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
Some Relations Between Schwarz–Pick Inequality and von Neumann’s Inequality 施瓦茨-皮克不等式与冯-诺依曼不等式之间的某些关系
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-05-10 DOI: 10.1007/s11785-024-01526-0
Kenta Kojin
{"title":"Some Relations Between Schwarz–Pick Inequality and von Neumann’s Inequality","authors":"Kenta Kojin","doi":"10.1007/s11785-024-01526-0","DOIUrl":"https://doi.org/10.1007/s11785-024-01526-0","url":null,"abstract":"<p>We study a Schwarz–Pick type inequality for the Schur–Agler class <span>(SA(B_{delta }))</span>. In our operator theoretical approach, von Neumann’s inequality for a class of generic tuples of <span>(2times 2)</span> matrices plays an important role rather than holomorphy. In fact, the class <span>(S_{2, gen}(B_{Delta }))</span> consisting of functions that satisfy the inequality for those matrices enjoys </p><span>$$begin{aligned} d_{mathbb {D}}(f(z), f(w))le d_{Delta }(z, w) ;;(z,win B_{Delta }, fin S_{2, gen}(B_{Delta })). end{aligned}$$</span><p>Here, <span>(d_{Delta })</span> is a function defined by a matrix <span>(Delta )</span> of functions. Later, we focus on the case when <span>(Delta )</span> is a matrix of holomorphic functions. We use the pseudo-distance <span>(d_{Delta })</span> to give a sufficient condition on a diagonalizable commuting tuple <i>T</i> acting on <span>(mathbb {C}^2)</span> for <span>(B_{Delta })</span> to be a complete spectral domain for <i>T</i>. We apply this sufficient condition to generalizing von Neumann’s inequalities studied by Drury (In: Blei RC, Sidney SJ (eds) Banach spaces, harmonic analysis, and probability theory, lecture notes in mathematics, vol 995. Springer, Berlin, pp 14–32, 1983) and by Hartz–Richter–Shalit (Math Z 301:3877–3894, 2022).</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"31 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140939104","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
Multivalued Elliptic Inclusion in Fractional Orlicz–Sobolev Spaces 分数 Orlicz-Sobolev 空间中的多值椭圆包容
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-05-09 DOI: 10.1007/s11785-024-01541-1
H. El-Houari, S. Hajar, H. Moussa
{"title":"Multivalued Elliptic Inclusion in Fractional Orlicz–Sobolev Spaces","authors":"H. El-Houari, S. Hajar, H. Moussa","doi":"10.1007/s11785-024-01541-1","DOIUrl":"https://doi.org/10.1007/s11785-024-01541-1","url":null,"abstract":"<p>In this research, we analyze the existence of nontrivial solution for a class of non-local multivalued elliptic problems on bounded domain with Direchlet boundary condition. The primary techniques employed consist of variational methods for Locally Lipschitz functional applied to fractional Orlicz–Sobolev space. Our main results generalize some recent findings in the literature to non-smooth cases.\u0000</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"24 18_suppl 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140939315","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
Hankel-Type Operator Acting on Hardy Spaces and Weighted Bergman Spaces 作用于哈代空间和加权伯格曼空间的汉克尔型算子
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-05-06 DOI: 10.1007/s11785-024-01539-9
Zhihui Zhou
{"title":"Hankel-Type Operator Acting on Hardy Spaces and Weighted Bergman Spaces","authors":"Zhihui Zhou","doi":"10.1007/s11785-024-01539-9","DOIUrl":"https://doi.org/10.1007/s11785-024-01539-9","url":null,"abstract":"<p>Inspired by Xiao’s work about the Hankel measures for the weighted Bergman spaces, in this paper, if <span>(beta &gt;0)</span> and the measure <span>(mu )</span> is a complex Borel measure on the unit disk <span>({mathbb {D}})</span>, we define the Hankel type operator <span>(K_{mu ,beta })</span> by </p><span>$$begin{aligned} K_{mu ,beta }:~flongmapsto int _{{mathbb {D}}}(1-wz)^{-(beta )}f(w)dmu (w). end{aligned}$$</span><p>The operator itself has been widely studied when <span>(mu )</span> is a positive Borel measure supported on the interval [0, 1). We study the boundedness of <span>(K_{mu ,1})</span> acting on Hardy spaces and the boundedness of <span>(K_{mu ,alpha })</span>, <span>(alpha &gt;1)</span> acting on weighted Bergman spaces. Then we raise and answer some questions about the boundedness of those operators. Also, we find some special measures <span>(mu 's)</span> such that <i>s</i>-Hankel measure is equal to <i>s</i>-Carleson measure.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"46 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889384","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
Fractional Gamma Noise Functionals 分数伽玛噪声函数
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-05-05 DOI: 10.1007/s11785-024-01534-0
Mohamed Ayadi, Anis Riahi, Mohamed Rhaima, Hamza Ghoudi
{"title":"Fractional Gamma Noise Functionals","authors":"Mohamed Ayadi, Anis Riahi, Mohamed Rhaima, Hamza Ghoudi","doi":"10.1007/s11785-024-01534-0","DOIUrl":"https://doi.org/10.1007/s11785-024-01534-0","url":null,"abstract":"<p>We construct an infinite dimensional analysis with respect to non-Gaussian measures of fractional Gamma type which we call fractional Gamma noise measures. It turns out that the well-known Wick ordered polynomials in Gaussian analysis cannot be generalized to this non-Gaussian case. Instead of using generalized Appell polynomials we prove that a system of biorthogonal polynomials, called Appell system, is applicable to the fractional Gamma measures. Finally, we gives some new properties of the kernels expressed in terms of the Stirling operators of the first and second kind as well as the falling factorials in infinite dimensions and we construct the so-called fractional Gamma noise Gel’fand triple.\u0000</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"67 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889260","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
Limiting Weak-Type Behavior of the Centered Hardy–Littlewood Maximal Function of General Measures on the Positive Real Line 正实线上一般度量的居中哈代-利特尔伍德最大函数的极限弱类型行为
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-05-03 DOI: 10.1007/s11785-024-01533-1
Wu-yi Pan, Sheng-jian Li
{"title":"Limiting Weak-Type Behavior of the Centered Hardy–Littlewood Maximal Function of General Measures on the Positive Real Line","authors":"Wu-yi Pan, Sheng-jian Li","doi":"10.1007/s11785-024-01533-1","DOIUrl":"https://doi.org/10.1007/s11785-024-01533-1","url":null,"abstract":"<p>Given a positive Borel measure <span>(mu )</span> on the one-dimensional Euclidean space <span>(textbf{R})</span>, consider the centered Hardy–Littlewood maximal function <span>(M_mu )</span> acting on a finite positive Borel measure <span>(nu )</span> by </p><span>$$begin{aligned} M_{mu }nu (x):=sup _{r&gt;r_0(x)}frac{nu (B(x,r))}{mu (B(x,r))},quad hbox { } xin textbf{R}, end{aligned}$$</span><p>where <span>(r_0(x) = inf {r&gt; 0: mu (B(x,r)) &gt; 0})</span> and <i>B</i>(<i>x</i>, <i>r</i>) denotes the closed ball with centre <i>x</i> and radius <span>(r &gt; 0)</span>. In this note, we restrict our attention to Radon measures <span>(mu )</span> on the positive real line <span>([0,+infty ))</span>. We provide a complete characterization of measures having weak-type asymptotic properties for the centered maximal function. Although we don’t know whether this fact can be extended to measures on the entire real line <span>(textbf{R})</span>, we examine some criteria for the existence of the weak-type asymptotic properties for <span>(M_mu )</span> on <span>(textbf{R})</span>. We also discuss further properties, and compute the value of the relevant asymptotic quantity for several examples of measures.\u0000</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"14 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889431","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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