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A Peak Set of Hausdorff Dimension 2n − 1 for the Algebra A(D) in the Boundary of a Domain D with C⌃2 Boundary 具有 C⌃2 边界的域 D 边界中代数 A(D) 的豪斯多夫维度为 2n - 1 的峰集
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-05-02 DOI: 10.1007/s11785-024-01532-2
Piotr Kot
{"title":"A Peak Set of Hausdorff Dimension 2n − 1 for the Algebra A(D) in the Boundary of a Domain D with C⌃2 Boundary","authors":"Piotr Kot","doi":"10.1007/s11785-024-01532-2","DOIUrl":"https://doi.org/10.1007/s11785-024-01532-2","url":null,"abstract":"<p>We consider a bounded strictly pseudoconvex domain <span>(Omega subset mathbb {C}^{n})</span> with <span>(C^{2})</span> boundary. Then, we show that any compact Ahlfors–David regular subset of <span>(partial Omega )</span> of Hausdorff dimension <span>(beta in (0,2n-1])</span> contains a peak set <i>E</i> of Hausdorff dimension equal to <span>(beta )</span>.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"106 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140842214","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
Orthogonal Exponential Functions on the Three-Dimensional Sierpinski Gasket 三维西尔平斯基垫圈上的正交指数函数
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-04-30 DOI: 10.1007/s11785-024-01536-y
Zhi-Min Wang
{"title":"Orthogonal Exponential Functions on the Three-Dimensional Sierpinski Gasket","authors":"Zhi-Min Wang","doi":"10.1007/s11785-024-01536-y","DOIUrl":"https://doi.org/10.1007/s11785-024-01536-y","url":null,"abstract":"<p>Let <span>(xi in mathbb {R})</span>, and <span>(rho _iin mathbb {R})</span> with <span>(0&lt;|rho _i|&lt;1)</span> for <span>(1le ile 3)</span>. For an expanding real matrix </p><span>$$begin{aligned} M=begin{bmatrix} rho _1^{-1}&amp;{}0&amp;{}xi 0&amp;{}rho _2^{-1}&amp;{}-xi 0&amp;{}0&amp;{}rho _3^{-1} end{bmatrix}in M_3(mathbb {R}) end{aligned}$$</span><p>and an integer digit set <span>(D={(0,0,0)^t, (1,0,0)^t, (0,1,0)^t, (0,0,1)^t }subset mathbb {Z}^3)</span>, let <span>(mu _{M,D})</span> be the self-affine measure defined by <span>(mu _{M,D}(cdot )=frac{1}{|D|}sum _{din D}mu _{M,D}(M(cdot )-d))</span>. In this paper, we prove that if <span>(rho _1=rho _2)</span>, then <span>(L^2(mu _{M,D}))</span> admits an infinite orthogonal set of exponential functions if and only if <span>(|rho _i|=(p_i/q_i)^{frac{1}{r_i}})</span> for some <span>(p_i,q_i,r_iin mathbb {N}^+)</span> with <span>(gcd (p_i,q_i)=1)</span> and <span>(2|q_i)</span>, <span>(i=1,2)</span>. In particular, if <span>(rho _1,rho _2,rho _3in {frac{p}{q}:p,qin 2mathbb {Z}+1})</span> and <span>(rho _1=rho _2)</span>, then there exist at most 4 mutually orthogonal exponential functions in <span>(L^2(mu _{M,D}))</span>, and the number 4 is the best.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"46 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140839945","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
Geometric Interpolation in n-Tuples of Noncommutative $$L_p$$ -Spaces 非交换 $$L_p$$ 空间 n 元组中的几何插值
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-04-30 DOI: 10.1007/s11785-024-01535-z
Feng Zhang
{"title":"Geometric Interpolation in n-Tuples of Noncommutative $$L_p$$ -Spaces","authors":"Feng Zhang","doi":"10.1007/s11785-024-01535-z","DOIUrl":"https://doi.org/10.1007/s11785-024-01535-z","url":null,"abstract":"<p>Let <span>(mathcal {M})</span> be a von Neumann algebra with a normal faithful semifinite trace. In this paper, we consider that in <i>n</i>-tuples of noncommutative <span>(L_p)</span>-spaces <span>(l_s^{(n)}(L_p(mathcal {M})))</span>, the norm is invariant under the action of invertible elements in <span>(mathcal {M})</span>. Then we prove that the complex interpolating theorem in the case of <span>(l_s^{(n)}(L_p(mathcal {M})))</span>. Using this result, we obtain that Clarkson’s inequalities for <i>n</i>-tuples of operators with weighted norm of noncommutative <span>(L_p)</span>-spaces, where the weight being a positive invertible operator in <span>(mathcal {M})</span>.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"20 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140839951","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
Almansi-Type Decomposition for Slice Regular Functions of Several Quaternionic Variables 多个四元变量的片正则函数的阿尔曼西式分解
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-04-29 DOI: 10.1007/s11785-024-01529-x
Giulio Binosi
{"title":"Almansi-Type Decomposition for Slice Regular Functions of Several Quaternionic Variables","authors":"Giulio Binosi","doi":"10.1007/s11785-024-01529-x","DOIUrl":"https://doi.org/10.1007/s11785-024-01529-x","url":null,"abstract":"<p>In this paper we propose an Almansi-type decomposition for slice regular functions of several quaternionic variables. Our method yields <span>(2^n)</span> distinct and unique decompositions for any slice function with domain in <span>(mathbb {H}^n)</span>. Depending on the choice of the decomposition, every component is given explicitly, uniquely determined and exhibits desirable properties, such as harmonicity and circularity in the selected variables. As consequences of these decompositions, we give another proof of Fueter’s Theorem in <span>(mathbb {H}^n)</span>, establish the biharmonicity of slice regular functions in every variable and derive mean value and Poisson formulas for them.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"1740 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140839966","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
Conformal Invariance of Clifford Monogenic Functions in the Indefinite Signature Case 无穷符号情况下克利福德单原函数的共形不变性
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-04-29 DOI: 10.1007/s11785-024-01528-y
Chen Liang, Matvei Libine
{"title":"Conformal Invariance of Clifford Monogenic Functions in the Indefinite Signature Case","authors":"Chen Liang, Matvei Libine","doi":"10.1007/s11785-024-01528-y","DOIUrl":"https://doi.org/10.1007/s11785-024-01528-y","url":null,"abstract":"<p>We extend constructions of classical Clifford analysis to the case of indefinite non-degenerate quadratic forms. Clifford analogues of complex holomorphic functions—called monogenic functions—are defined by means of the Dirac operators that factor a certain wave operator. One of the fundamental features of quaternionic analysis is the invariance of quaternionic analogues of holomorphic function under conformal (or Möbius) transformations. A similar invariance property is known to hold in the context of Clifford algebras associated to positive definite quadratic forms. We generalize these results to the case of Clifford algebras associated to all non-degenerate quadratic forms. This result puts the indefinite signature case on the same footing as the classical positive definite case.\u0000</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"15 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140839786","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
Characterizations of Finite Order Solutions of Circular Type Partial Differential-Difference Equations in $$ mathbb {C}^n $$ $$ mathbb {C}^n $$ 中循环型偏微分-差分方程的有限阶解的特征
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-04-27 DOI: 10.1007/s11785-024-01530-4
Sanju Mandal, Molla Basir Ahamed
{"title":"Characterizations of Finite Order Solutions of Circular Type Partial Differential-Difference Equations in $$ mathbb {C}^n $$","authors":"Sanju Mandal, Molla Basir Ahamed","doi":"10.1007/s11785-024-01530-4","DOIUrl":"https://doi.org/10.1007/s11785-024-01530-4","url":null,"abstract":"<p>This paper employs Nevanlinna value distribution theory in several complex variables to explore the characteristics and form of finite as well as infinite order solutions of Circular-type nonlinear partial differential-difference equations in <span>(mathbb {C}^n)</span>. The results obtained in this paper contribute to the improvement and generalization of some recent results. In addition, illustrative examples are provided to validate the conclusions drawn from the main results. Moreover, we investigate the infinite-order solutions of Circular-type functional equations in <span>( mathbb {C}^n )</span>.\u0000</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"73 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140809054","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
Matrix Mean Inequalities for Sector Matrices 扇形矩阵的矩阵均值不等式
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-04-26 DOI: 10.1007/s11785-024-01531-3
Maryam Khosravi, Alemeh Sheikhhosseini, Somayeh Malekinejad
{"title":"Matrix Mean Inequalities for Sector Matrices","authors":"Maryam Khosravi, Alemeh Sheikhhosseini, Somayeh Malekinejad","doi":"10.1007/s11785-024-01531-3","DOIUrl":"https://doi.org/10.1007/s11785-024-01531-3","url":null,"abstract":"<p>In this note, some inequalities involving matrix means of sectorial matrices are proved which are generalizations and refinements of previous known results. Among them, let <i>A</i> and <i>B</i> be two accretive matrices with <span>(A,Bin mathcal {S}_{theta })</span>, <span>(0 &lt; mI leqslant A, B leqslant MI)</span> for positive real numbers <i>M</i> and <i>m</i>. If <span>(sigma ,sigma _1,sigma _2)</span> are matrix means such that <span>(sigma ^*leqslant sigma _1,sigma _2leqslant sigma )</span>, where <span>(sigma ^*)</span> is the adjoint of <span>(sigma )</span> and <span>(Phi )</span> is a positive unital linear map, then for each <span>(p&gt;0)</span>, </p><span>$$Phi ^{p}Re (A sigma _{1} B) leqslant sec ^{2p}theta alpha ^{p} Phi ^{p}Re (A sigma _{2} B),$$</span><p>where </p><span>$$ alpha = max left{ K, 4^{1-frac{2}{p}}K right} ,$$</span><p>and <span>( K= frac{(M+m)^2}{4mM})</span> is the Kantorovich constant.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140805715","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
Automorphic Carathéodory–Julia Theorem 自动卡拉瑟奥多里-朱利亚定理
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-04-22 DOI: 10.1007/s11785-024-01527-z
Alexander Kheifets
{"title":"Automorphic Carathéodory–Julia Theorem","authors":"Alexander Kheifets","doi":"10.1007/s11785-024-01527-z","DOIUrl":"https://doi.org/10.1007/s11785-024-01527-z","url":null,"abstract":"<p>Let <span>(w(zeta ))</span> be a function analytic on <span>({{mathbb {D}}})</span>, <span>(|w(zeta )|le 1)</span>. Let <span>(|t_0|=1)</span>. Assume that <i>w</i> and <span>(w')</span> have nontangential boundary values <span>(w_0)</span> and <span>(w'_0)</span>, respectively, at <span>(t_0)</span>, <span>(|w_0|=1)</span>. Then (Carathéodory–Julia) <span>(t_0dfrac{w'_0}{w_0}ge 0)</span>. The goal of this paper is to obtain a lower bound on this ratio if <i>w</i> is character-automorphic with respect to a Fuchsian group (Theorem 6.1).</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"133 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140805712","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
Weyl Sets in a Non-degenerate Truncated Matricial Hausdorff Moment Problem 非退化截断矩豪斯多夫矩问题中的韦尔集
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-04-17 DOI: 10.1007/s11785-024-01525-1
Max Heide, Bernd Fritzsche, Bernd Kirstein, Conrad Mädler
{"title":"Weyl Sets in a Non-degenerate Truncated Matricial Hausdorff Moment Problem","authors":"Max Heide, Bernd Fritzsche, Bernd Kirstein, Conrad Mädler","doi":"10.1007/s11785-024-01525-1","DOIUrl":"https://doi.org/10.1007/s11785-024-01525-1","url":null,"abstract":"<p>Given a point <i>w</i> in the upper half-plane <span>(Pi _{mathord {+}})</span>, we describe the set of all possible values <i>F</i>(<i>w</i>) of transforms <span>(F(z),{:=},int _{[alpha ,beta ]}(x-z)^{-1}sigma (textrm{d}x))</span>, <span>(zin Pi _{mathord {+}})</span>, corresponding to solutions <span>(sigma )</span> to a (non-degenerate) truncated matricial Hausdorff moment problem. This set turns out to be the intersection of two matrix balls the parameters of which are explicitly constructed from the given data.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"161 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140609024","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
Sequences of Operators, Monotone in the Sense of Contractive Domination 操作数序列，收缩支配意义上的单调性
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-04-15 DOI: 10.1007/s11785-024-01507-3
S. Hassi, H. S. V. de Snoo
{"title":"Sequences of Operators, Monotone in the Sense of Contractive Domination","authors":"S. Hassi, H. S. V. de Snoo","doi":"10.1007/s11785-024-01507-3","DOIUrl":"https://doi.org/10.1007/s11785-024-01507-3","url":null,"abstract":"<p>A sequence of operators <span>(T_n)</span> from a Hilbert space <span>({{mathfrak {H}}})</span> to Hilbert spaces <span>({{mathfrak {K}}}_n)</span> which is nondecreasing in the sense of contractive domination is shown to have a limit which is still a linear operator <i>T</i> from <span>({{mathfrak {H}}})</span> to a Hilbert space <span>({{mathfrak {K}}})</span>. Moreover, the closability or closedness of <span>(T_n)</span> is preserved in the limit. The closures converge likewise and the connection between the limits is investigated. There is no similar way of dealing directly with linear relations. However, the sequence of closures is still nondecreasing and then the convergence is governed by the monotonicity principle. There are some related results for nonincreasing sequences.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"53 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140609031","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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