Computational Methods and Function Theory最新文献

On Uniformity Exponents of $$varphi $$ -Uniform Domains 论 $$varphi $$ -Uniform 域的均匀性指数

IF 2.1 4区数学

Computational Methods and Function Theory Pub Date : 2024-09-11 DOI: 10.1007/s40315-024-00561-4

Yahui Sheng, Fan Wen, Kai Zhan

引用次数: 0

Hilbert-Type Operators Acting on Bergman Spaces 作用于伯格曼空间的希尔伯特型算子

IF 2.1 4区数学

Computational Methods and Function Theory Pub Date : 2024-09-02 DOI: 10.1007/s40315-024-00560-5

Tanausú Aguilar-Hernández, Petros Galanopoulos, Daniel Girela

{"title":"Hilbert-Type Operators Acting on Bergman Spaces","authors":"Tanausú Aguilar-Hernández, Petros Galanopoulos, Daniel Girela","doi":"10.1007/s40315-024-00560-5","DOIUrl":"https://doi.org/10.1007/s40315-024-00560-5","url":null,"abstract":"If (mu ) is a positive Borel measure on the interval [0, 1) we let ({mathcal {H}}_mu ) be the Hankel matrix ({mathcal {H}}_mu =(mu _{n, k})_{n,kge 0}) with entries (mu _{n, k}=mu _{n+k}), where, for (n,=,0, 1, 2, ldots ), (mu _n) denotes the moment of order n of (mu ). This matrix formally induces an operator, called also ({mathcal {H}}_mu ), on the space of all analytic functions in the unit disc ({mathbb {D}}) as follows: If f is an analytic function in ({mathbb {D}}), (f(z)=sum _{k=0}^infty a_kz^k), (zin {{mathbb {D}}}), ({mathcal {H}}_mu (f)) is formally defined by $$begin{aligned} {mathcal {H}}_mu (f)(z)= sum _{n=0}^{infty }left( sum _{k=0}^{infty } mu _{n+k}{a_k}right) z^n,quad zin {mathbb {D}}. end{aligned}$$This is a natural generalization of the classical Hilbert operator. This paper is devoted to studying the operators (H_mu ) acting on the Bergman spaces (A^p), (1le p<infty ). Among other results, we give a complete characterization of those (mu ) for which ({mathcal {H}}_mu ) is bounded or compact on the space (A^p) when p is either 1 or greater than 2. We also give a number of results concerning the boundedness and compactness of (mathcal H_mu ) on (A^p) for the other values of p, as well as on its membership in the Schatten classes ({mathcal {S}}_p(A^2)).","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218024","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

A Characterization of Concave Mappings Using the Carathéodory Class and Schwarzian Derivative 利用卡拉瑟奥多里类和施瓦兹衍生物表征凹映射

IF 2.1 4区数学

Computational Methods and Function Theory Pub Date : 2024-08-22 DOI: 10.1007/s40315-024-00557-0

Víctor Bravo, Rodrigo Hernández, Osvaldo Venegas

引用次数: 0

The $$*$$ -Exponential as a Covering Map 作为覆盖图的 $$*$$ - 指数

IF 2.1 4区数学

Computational Methods and Function Theory Pub Date : 2024-08-17 DOI: 10.1007/s40315-024-00558-z

Amedeo Altavilla, Samuele Mongodi

引用次数: 0

Entire Solutions of Certain Type Binomial Differential Equations 某些类型二项式微分方程的全解

IF 2.1 4区数学

Computational Methods and Function Theory Pub Date : 2024-08-09 DOI: 10.1007/s40315-024-00556-1

Shuang-Shuang Yang, Liang-Wen Liao, Xiao-Qing Lu

引用次数: 0

The Generic Failure of Lower-Semicontinuity for the Linear Distortion Functional 线性失真函数的下半连续性一般失效

IF 2.1 4区数学

Computational Methods and Function Theory Pub Date : 2024-08-07 DOI: 10.1007/s40315-024-00555-2

Mohsen Hashemi, Gaven J. Martin

{"title":"The Generic Failure of Lower-Semicontinuity for the Linear Distortion Functional","authors":"Mohsen Hashemi, Gaven J. Martin","doi":"10.1007/s40315-024-00555-2","DOIUrl":"https://doi.org/10.1007/s40315-024-00555-2","url":null,"abstract":"We consider the convexity properties of distortion functionals, particularly the linear distortion, defined for homeomorphisms of domains in Euclidean n-spaces, (nge 3). The inner and outer distortion functionals are lower semi-continuous in all dimensions and so for the curve modulus or analytic definitions of quasiconformality it ifollows that if ( { f_{n} }_{n=1}^{infty } ) is a sequence of K-quasiconformal mappings (here K depends on the particular distortion functional but is the same for every element of the sequence) which converges locally uniformly to a mapping f, then this limit function is also K-quasiconformal. Despite a widespread belief that this was also true for the geometric definition of quasiconformality (defined through the linear distortion (H({f_{n}}))), T. Iwaniec gave a specific and surprising example to show that the linear distortion functional is not always lower-semicontinuous on uniformly converging sequences of quasiconformal mappings. Here we show that this failure of lower-semicontinuity is common, perhaps generic in the sense that under mild restrictions on a quasiconformal f, there is a sequence ( {f_{n} }_{n=1}^{infty } ) with ( {f_{n}}rightarrow {f}) locally uniformly and with (limsup _{nrightarrow infty } H( {f_{n}})<H( {f})). Our main result shows this is true for affine mappings. Addressing conjectures of Gehring and Iwaniec we show the jump up in the limit can be arbitrarily large and give conjecturally sharp bounds: for each (alpha <sqrt{2}) there is ({f_{n}}rightarrow {f}) locally uniformly with f affine and $$begin{aligned} alpha ; limsup _{nrightarrow infty } H( {f_{n}}) < H( {f}) end{aligned}$$We conjecture (sqrt{2}) to be best possible.","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141934029","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 Linear Dilatation of the Mappings Satisfying an Inverse Poletsky Modular Inequality in Metric Spaces 论公设空间中满足逆波列茨基模量不等式的映射的线性稀疏化

IF 2.1 4区数学

Computational Methods and Function Theory Pub Date : 2024-07-03 DOI: 10.1007/s40315-024-00553-4

Mihai Cristea

引用次数: 0

A Bessel Analog of the Riesz Composition Formula 里兹合成公式的贝塞尔类似公式

IF 2.1 4区数学

Computational Methods and Function Theory Pub Date : 2024-07-02 DOI: 10.1007/s40315-024-00539-2

Christoph Fischbacher, Fritz Gesztesy, Roger Nichols

引用次数: 0

Diameter of Compact Riemann Surfaces 紧凑黎曼曲面的直径

IF 2.1 4区数学

Computational Methods and Function Theory Pub Date : 2024-06-27 DOI: 10.1007/s40315-024-00546-3

Huck Stepanyants, Alan Beardon, Jeremy Paton, Dmitri Krioukov

引用次数: 0

On the Poincaré Inequality on Open Sets in $$mathbb {R}^n$$ 论 $$mathbb {R}^n$$ 中开放集上的 Poincaré 不等式

IF 2.1 4区数学

Computational Methods and Function Theory Pub Date : 2024-06-26 DOI: 10.1007/s40315-024-00550-7

A.-K. Gallagher

引用次数: 0