Complex Analysis and Operator Theory最新文献_第4页

On the Expansion of Resolvents and the Integrated Density of States for Poisson Distributed Schrödinger Operators 论泊松分布式薛定谔算子的残留物展开和综合状态密度

IF 0.8 4区数学

Complex Analysis and Operator Theory Pub Date : 2024-07-04 DOI: 10.1007/s11785-024-01546-w

David Hasler, Jannis Koberstein

引用次数: 0

On the Differentiation of Integrals in Measure Spaces Along Filters: II 论沿着滤波器的测度空间积分微分：二

IF 0.8 4区数学

Complex Analysis and Operator Theory Pub Date : 2024-07-03 DOI: 10.1007/s11785-024-01552-y

Fausto Di Biase, Steven G. Krantz

{"title":"On the Differentiation of Integrals in Measure Spaces Along Filters: II","authors":"Fausto Di Biase, Steven G. Krantz","doi":"10.1007/s11785-024-01552-y","DOIUrl":"https://doi.org/10.1007/s11785-024-01552-y","url":null,"abstract":"Let X be a complete measure space of finite measure. The Lebesgue transform of an integrable function f on X encodes the collection of all the mean-values of f on all measurable subsets of X of positive measure. In the problem of the differentiation of integrals, one seeks to recapture f from its Lebesgue transform. In previous work we showed that, in all known results, f may be recaptured from its Lebesgue transform by means of a limiting process associated to an appropriate family of filters defined on the collection ({{,mathrm{{mathcal {A}}},}}) of all measurable subsets of X of positive measure. The first result of the present work is that the existence of such a limiting process is equivalent to the existence of a Von Neumann-Maharam lifting of X. In the second result of this work we provide an independent argument that shows that the recourse to filters is a necessary consequence of the requirement that the process of recapturing f from its mean-values is associated to a natural transformation, in the sense of category theory. This result essentially follows from the Yoneda lemma. As far as we know, this is the first instance of a significant interaction between category theory and the problem of the differentiation of integrals. In the Appendix we have proved, in a precise sense, that natural transformations fall within the general concept of homomorphism. As far as we know, this is a novel conclusion: Although it is often said that natural transformations are homomorphisms of functors, this statement appears to be presented as a mere analogy, not in a precise technical sense. In order to achieve this result, we had to bring to the foreground a notion that is implicit in the subject but has remained hidden in the background, i.e., that of partial magma.","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"31 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141547851","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

Toeplitz Operators Associated with the Hypergeometric Gabor Transform and Applications 与超几何 Gabor 变换相关的托普利兹算子及其应用

IF 0.8 4区数学

Complex Analysis and Operator Theory Pub Date : 2024-07-01 DOI: 10.1007/s11785-024-01569-3

Hatem Mejjaoli

引用次数: 0

S-Nodes, Factorisation of Spectral Matrix Functions and Corresponding Inequalities S 节点、谱矩阵函数因式分解及相应不等式

IF 0.8 4区数学

Complex Analysis and Operator Theory Pub Date : 2024-07-01 DOI: 10.1007/s11785-024-01567-5

Alexander Sakhnovich

引用次数: 0

Characterization of Forward, Vanishing, and Reverse Bergman Carleson Measures using Sparse Domination 利用稀疏主宰法表征正向、消失和反向伯格曼-卡列松量纲

IF 0.8 4区数学

Complex Analysis and Operator Theory Pub Date : 2024-06-28 DOI: 10.1007/s11785-024-01565-7

Hamzeh Keshavarzi

引用次数: 0

Commutativity and Compactness of kth Order Slant Toeplitz Operators k 阶斜托普利兹算子的交换性与紧凑性

IF 0.8 4区数学

Complex Analysis and Operator Theory Pub Date : 2024-06-27 DOI: 10.1007/s11785-024-01570-w

M. Premjit Singh, Khumballambam Priyobarta Singh, Elija Chongtham, Oinam Nilbir Singh

引用次数: 0

A Nagy–Foias Program for a C.N.U. $$Gamma _n$$ -Contraction C.N.U. $$Gamma _n$$ -协约的纳吉-福阿斯程序

IF 0.8 4区数学

Complex Analysis and Operator Theory Pub Date : 2024-06-27 DOI: 10.1007/s11785-024-01568-4

Bappa Bisai, Sourav Pal

{"title":"A Nagy–Foias Program for a C.N.U. $$Gamma _n$$ -Contraction","authors":"Bappa Bisai, Sourav Pal","doi":"10.1007/s11785-024-01568-4","DOIUrl":"https://doi.org/10.1007/s11785-024-01568-4","url":null,"abstract":"A tuple of commuting Hilbert space operators ((S_1, ldots , S_{n-1}, P)) having the closed symmetrized polydisc $$begin{aligned} Gamma _n = left{ left( sum _{i=1}^{n}z_i, sum limits _{1le i<jle n} z_iz_j, ldots , prod _{i=1}^{n}z_iright) : |z_i|le 1, ; ; ; 1le i le n-1 right} end{aligned}$$as a spectral set is called a (Gamma _n)-contraction. From the literature we have that a point ((s_1, ldots , s_{n-1},p)) in (Gamma _n) can be represented as (s_i=c_i+pc_{n-i}) for some ((c_1, ldots , c_{n-1}) in Gamma _{n-1}). We construct a minimal (Gamma _n)-isometric dilation for a particular class of c.n.u. (Gamma _n)-contractions ((S_1, ldots , S_{n-1},P)) and obtain a functional model for them. With the help of this model we express each (S_i) as (S_i=C_i+PC_{n-i}), which is an operator theoretic analogue of the scalar result. We also produce an abstract model for a different class of c.n.u. (Gamma _n)-contractions satisfying (S_i^*P=PS_i^*) for each i. By exhibiting a counter example we show that such abstract model may not exist if we drop the hypothesis that (S_i^*P=PS_i^*). We apply this abstract model to achieve a complete unitary invariant for such c.n.u. (Gamma _n)-contractions. Additionally, we present different necessary conditions for dilation and a sufficient condition under which a commuting tuple ((S_1, ldots , S_{n-1},P)) becomes a (Gamma _n)-contraction. The entire program goes parallel to the operator theoretic program developed by Sz.-Nagy and Foias for a c.n.u. contraction.","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"28 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509721","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 Monotony of Struve Functions 论斯特鲁夫函数的单调性

IF 0.8 4区数学

Complex Analysis and Operator Theory Pub Date : 2024-06-25 DOI: 10.1007/s11785-024-01563-9

Erhan Deniz, Róbert Szász

引用次数: 0

Dirichlet Problem for Nonlinear Higher-Order Equations in Upper Half Plane 上半平面非线性高阶方程的 Dirichlet 问题

IF 0.8 4区数学

Complex Analysis and Operator Theory Pub Date : 2024-06-25 DOI: 10.1007/s11785-024-01566-6

Pelin Ayşe Gökgöz

引用次数: 0

A Gap Condition for the Zeros and Singularities of a Certain Class of Products 某类积的零点和奇点的间隙条件