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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
Controllability of Mild Solutions for Second-Order Neutral Evolution Equations with State-Dependent Delay 具有状态延迟的二阶中性演化方程温和解的可控性
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-04-10 DOI: 10.1007/s11785-024-01524-2
Chahrazed Boudefla, Fatiha Sahraoui, Selma Baghli-Bendimerad
{"title":"Controllability of Mild Solutions for Second-Order Neutral Evolution Equations with State-Dependent Delay","authors":"Chahrazed Boudefla, Fatiha Sahraoui, Selma Baghli-Bendimerad","doi":"10.1007/s11785-024-01524-2","DOIUrl":"https://doi.org/10.1007/s11785-024-01524-2","url":null,"abstract":"<p>The objective of our research is to demonstrate the controllability of mild solutions for a specific class of second-order neutral functional evolution equations that involve state-dependent delay. To achieve this, we rely on Avramescu’s nonlinear alternative theorem and leverage cosine function theory.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"298 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140593637","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
$$Llog L$$ Type Estimates for Commutators of Fractional Integral Operators on the p-Adic Vector Space p-Adic 向量空间上分式积分算子的换元数的 $$Llog L$$ 型估计值
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-04-09 DOI: 10.1007/s11785-024-01514-4
YunPeng Chang, LiangJuan Yu, LinQi Sun, HuangZhi Xia
{"title":"$$Llog L$$ Type Estimates for Commutators of Fractional Integral Operators on the p-Adic Vector Space","authors":"YunPeng Chang, LiangJuan Yu, LinQi Sun, HuangZhi Xia","doi":"10.1007/s11785-024-01514-4","DOIUrl":"https://doi.org/10.1007/s11785-024-01514-4","url":null,"abstract":"<p>In this paper, the main aim is to prove the weak type <span>(L log L)</span> estimates for commutators of fractional integral operators and the higher order in the context of the <i>p</i>-adic version of Lebesgue spaces, where the symbols of the commutators belong to the <i>p</i>-adic version of <span>({text {BMO}})</span> space. In addition, we also establish the estimates of the sharp function on the <i>p</i>-adic vector space.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"155 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140603309","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
Hilbert Transform, Nevanlinna Class and Toeplitz Kernels 希尔伯特变换、内万林纳类和托普利兹核
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-04-07 DOI: 10.1007/s11785-024-01521-5
Arun K. Bhardwaj, Javad Mashreghi, R. K. Srivastava
{"title":"Hilbert Transform, Nevanlinna Class and Toeplitz Kernels","authors":"Arun K. Bhardwaj, Javad Mashreghi, R. K. Srivastava","doi":"10.1007/s11785-024-01521-5","DOIUrl":"https://doi.org/10.1007/s11785-024-01521-5","url":null,"abstract":"<p>In this article we obtain an explicit formula for the Hilbert transform of <span>(log |f|,)</span> for the function <i>f</i> in Nevanlinna class having continuous extension to the real line. This family is the largest possible for which such a formula for the Hilbert transform of <span>(log |f|,)</span> can be obtained. The formula is very general and implies several previously known results.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"100 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140593470","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
b-AM-Dunford–Pettis Operators on Banach lattices 巴拿赫网格上的 b-AM-Dunford-Pettis 算子
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-04-06 DOI: 10.1007/s11785-024-01523-3
Hamadi Baklouti, Mohamed Hajji, Radhouene Moulahi
{"title":"b-AM-Dunford–Pettis Operators on Banach lattices","authors":"Hamadi Baklouti, Mohamed Hajji, Radhouene Moulahi","doi":"10.1007/s11785-024-01523-3","DOIUrl":"https://doi.org/10.1007/s11785-024-01523-3","url":null,"abstract":"<p>In our research work, we introduce a new class of operators that we call <i>b</i>-<i>AM-Dunford–Pettis</i> operators. Properties of <i>b</i>-AM-Dunford–Pettis operators, the relationship between the <i>b</i>-AM-Dunford–Pettis operators and various classes of operators are investigated. On the other side, our techniques and results will be related to the lattice structure of the <i>b</i>-AM-Dunford–Pettis operators. For instance, it will be proved that under certain conditions, the <i>b</i>-AM-Dunford–Pettis opertors verify the domination properties.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140570508","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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