Computational Methods and Function Theory最新文献_第5页

Estimates of Partial Derivatives for Harmonic Functions on the Unit Disc 单位圆盘上谐函数偏导数的估计值

IF 2.1 4区数学

Computational Methods and Function Theory Pub Date : 2023-12-22 DOI: 10.1007/s40315-023-00514-3

{"title":"Estimates of Partial Derivatives for Harmonic Functions on the Unit Disc","authors":"","doi":"10.1007/s40315-023-00514-3","DOIUrl":"https://doi.org/10.1007/s40315-023-00514-3","url":null,"abstract":"<h3>Abstract</h3> Let (f = P[F]) denote the Poisson integral of F in the unit disc ({{mathbb {D}}}) with F absolutely continuous on the unit circle ({{mathbb {T}}}) and (dot{F}in L^p({{mathbb {T}}})) , where (dot{F}(e^{it}) = frac{d}{dt} F(e^{it})) . We show that for (pin (1,infty )) , the partial derivatives (f_z) and (overline{f_{bar{z}}}) belong to the holomorphic Hardy space (H^p({{mathbb {D}}})) . In addition, for (p=1) or (p=infty ) , (f_z) and (overline{f_{bar{z}}}in H^p({{mathbb {D}}})) if and only if (H(dot{F})in L^p({{mathbb {T}}})) , the Hilbert transform of (dot{F}) and in that case, we have (2izf_z=P[dot{F}+iH(dot{F})]) . Our main tools are integral representations of (f_z) and (f_{overline{z}}) in terms of (dot{F}) and M. Riesz’s theorem on conjugate functions. This simplifies and extends the recent results of Chen et al. [1] (J. Geom. Anal., 2021) and Zhu [17] (J. Geom. Anal., 2021).","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":"55 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139028877","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

Almost Periodic Functions: Their Limit Sets and Various Applications 几乎周期函数：它们的极限集和各种应用

IF 2.1 4区数学

Computational Methods and Function Theory Pub Date : 2023-12-22 DOI: 10.1007/s40315-023-00515-2

Lev Sakhnovich

引用次数: 0

Best Möbius Approximations of Convex and Concave Mappings 凸贴图和凹贴图的最佳莫比乌斯近似值

IF 2.1 4区数学

Computational Methods and Function Theory Pub Date : 2023-12-12 DOI: 10.1007/s40315-023-00517-0

Martin Chuaqui, Brad Osgood

引用次数: 0

Julia Sets, Jordan Curves and Quasi-circles 茱莉亚集，乔丹曲线和准圆

IF 2.1 4区数学

Computational Methods and Function Theory Pub Date : 2023-11-30 DOI: 10.1007/s40315-023-00512-5

Norbert Steinmetz

引用次数: 0

Lattice Paths, Vector Continued Fractions, and Resolvents of Banded Hessenberg Operators 点阵路径，向量连分数，和带状Hessenberg算子的解

IF 2.1 4区数学

Computational Methods and Function Theory Pub Date : 2023-11-24 DOI: 10.1007/s40315-023-00511-6

A. López-García, V. A. Prokhorov

{"title":"Lattice Paths, Vector Continued Fractions, and Resolvents of Banded Hessenberg Operators","authors":"A. López-García, V. A. Prokhorov","doi":"10.1007/s40315-023-00511-6","DOIUrl":"https://doi.org/10.1007/s40315-023-00511-6","url":null,"abstract":"We give a combinatorial interpretation of vector continued fractions obtained by applying the Jacobi–Perron algorithm to a vector of (pge 1) resolvent functions of a banded Hessenberg operator of order (p+1). The interpretation consists in the identification of the coefficients in the power series expansion of the resolvent functions as weight polynomials associated with Lukasiewicz lattice paths in the upper half-plane. In the scalar case (p=1) this reduces to the relation established by P. Flajolet and G. Viennot between Jacobi–Stieltjes continued fractions, their power series expansion, and Motzkin paths. We consider three classes of lattice paths, namely the Lukasiewicz paths in the upper half-plane, their symmetric images in the lower half-plane, and a third class of unrestricted lattice paths which are allowed to cross the x-axis. We establish a relation between the three families of paths by means of a relation between the associated generating power series. We also discuss the subcollection of Lukasiewicz paths formed by the partial p-Dyck paths, whose weight polynomials are known in the literature as genetic sums or generalized Stieltjes–Rogers polynomials, and express certain moments of bi-diagonal Hessenberg operators.","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":"326 ","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138519707","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: 1

A Difference Version of the Rubel-Yang–Mues-Steinmetz–Gundersen Theorem Rubel-Yang-Mues-Steinmetz-Gundersen定理的一个不同版本

IF 2.1 4区数学

Computational Methods and Function Theory Pub Date : 2023-11-24 DOI: 10.1007/s40315-023-00510-7

Mingliang Fang, Hui Li, Wenqiang Shen, Xiao Yao

引用次数: 0

The Sharp Distortion Estimate Concerning Julia’s Lemma 关于茱莉亚引理的急剧失真估计

IF 2.1 4区数学

Computational Methods and Function Theory Pub Date : 2023-11-21 DOI: 10.1007/s40315-023-00505-4

Shota Hoshinaga, Hiroshi Yanagihara

{"title":"The Sharp Distortion Estimate Concerning Julia’s Lemma","authors":"Shota Hoshinaga, Hiroshi Yanagihara","doi":"10.1007/s40315-023-00505-4","DOIUrl":"https://doi.org/10.1007/s40315-023-00505-4","url":null,"abstract":"For (alpha > 0), let (J_alpha ) be the class of all analytic functions f in the unit disk ({mathbb {D}}: = { z in {mathbb {C}}: |z| < 1 }) satisfying (f({mathbb {D}}) subset {mathbb {D}}) with the the angular derivative $$begin{aligned} angle lim _{z rightarrow 1} frac{f(z)-1}{z-1} = alpha . end{aligned}$$For (a,zin mathbb {D}), let $$begin{aligned} k(z) = frac{|1-z|^2}{1-|z|^2}quad text {and}quad sigma _a(z) = frac{1-overline{a}}{1-a} frac{z-a}{1-overline{a}z}. end{aligned}$$Let (z_0 in {mathbb {D}}) be fixed. For (f in J_alpha ), we obtain the sharp estimate $$begin{aligned} |f'(z_0)| le frac{4 alpha k(z_0)^2}{(alpha k(z_0)+1)^2 |1-z_0|^2} qquad text {when }alpha k(z_0) le 1, end{aligned}$$with equality if and only if (f = sigma _{w_0}^{-1} circ sigma _{z_0}). Here (w_0 = (1-alpha k(z_0))/(alpha k(z_0) +1)). In case of (alpha k(z_0) > 1) we derive the estimate (|f'(z_0)| le k(z_0)/|1-z_0|^2). It is also sharp, however in contrast to the former case, there are no extremal functions in (J_alpha ). The lack of extremal functions is caused by the fact that (J_alpha ) is not closed in the topology of local uniform convergence in ({mathbb {D}}). Thus we consider the closure (bar{J}_alpha ) of (J_alpha ) and study (bar{V}_1(z_0, alpha ):= { f'(z_0): f in bar{J}_alpha }) which is the variability region of (f'(z_0)) when f ranges over (bar{J}_alpha ). We shall show that (partial bar{V}_1(z_0, alpha )) is a simple closed curve and (bar{V}_1(z_0, alpha )) is a convex and closed Jordan domain enclosed by (partial bar{V}_1(z_0, alpha )). Moreover, we shall give a parametric representation of (partial bar{V}_1(z_0, alpha )) and determine all extremal functions.","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":"335 ","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138519704","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 Forms of Meromorphic Solutions of Some Type of Non-linear Differential Equations 一类非线性微分方程亚纯解的形式

4区数学

Computational Methods and Function Theory Pub Date : 2023-11-11 DOI: 10.1007/s40315-023-00509-0

Huifang Liu, Zhiqiang Mao

引用次数: 0

On the Teichmüller–Nitsche Problem of T. Iwaniec, L.V. Kovalev, and J. Onninen 论T.伊万涅茨、L.V.科瓦列夫和J.奥尼宁的技术<s:1>米勒-尼采问题

4区数学

Computational Methods and Function Theory Pub Date : 2023-10-17 DOI: 10.1007/s40315-023-00504-5

Daoud Bshouty, Abdallah Lyzzaik

引用次数: 0

Successive Logarithmic Coefficients of Univalent Functions 一元函数的连续对数系数

4区数学

Computational Methods and Function Theory Pub Date : 2023-10-11 DOI: 10.1007/s40315-023-00500-9

Adam Lecko, Dariusz Partyka

{"title":"Successive Logarithmic Coefficients of Univalent Functions","authors":"Adam Lecko, Dariusz Partyka","doi":"10.1007/s40315-023-00500-9","DOIUrl":"https://doi.org/10.1007/s40315-023-00500-9","url":null,"abstract":"Abstract The paper deals with logarithmic coefficients of univalent functions. The sharp lower and upper estimations of $$|gamma _2(f)|-|gamma _1(f)|$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mrow> <mml:mo>|</mml:mo> </mml:mrow> <mml:msub> <mml:mi>γ</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>f</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>|</mml:mo> <mml:mo>-</mml:mo> <mml:mo>|</mml:mo> </mml:mrow> <mml:msub> <mml:mi>γ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>f</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>|</mml:mo> </mml:mrow> </mml:mrow> </mml:math> were obtained in the class $${mathcal {S}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>S</mml:mi> </mml:math> , where $$gamma _n(f)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>γ</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>f</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> denotes the n -th logarithmic coefficient of $$fin {mathcal {S}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>S</mml:mi> </mml:mrow> </mml:math> . The result is applicable to some standard subclasses of $${mathcal {S}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>S</mml:mi> </mml:math> . Relevant examples were indicated.","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":"116 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136059354","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