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Complex Variables, Theory and Application: An International Journal最新文献

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Mapping onto circular arc polygons 映射到圆弧多边形
Complex Variables, Theory and Application: An International Journal Pub Date : 2005-02-10 DOI: 10.1080/02781070412331329403
P. R. Brown
{"title":"Mapping onto circular arc polygons","authors":"P. R. Brown","doi":"10.1080/02781070412331329403","DOIUrl":"https://doi.org/10.1080/02781070412331329403","url":null,"abstract":"A numerical method is developed for computing the accessory parameter of the Schwarzian derivative of the univalent mappings onto certain circular arc polygons with orthogonal boundary arcs. The geometrical properties of these polygons are investigated rigorously. An application of this method makes it possible to compute numerically the hyperbolic metric density function for some multiply-connected planar domains; in particular the covering map of the plane minus a lattice of discs.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"15 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120862533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
Distortion theorems for biholomorphic convex mappings in Banach spaces* Banach空间*中生物全纯凸映射的畸变定理
Complex Variables, Theory and Application: An International Journal Pub Date : 2005-01-15 DOI: 10.1080/02781070412331329412
Yu-Can Zhu, Mingsheng Liu †
{"title":"Distortion theorems for biholomorphic convex mappings in Banach spaces*","authors":"Yu-Can Zhu, Mingsheng Liu †","doi":"10.1080/02781070412331329412","DOIUrl":"https://doi.org/10.1080/02781070412331329412","url":null,"abstract":"In this article, we give some distortion theorems for biholomorphic convex mappings in Banach spaces and Hilbert spaces. In particular, we prove that the conjecture of Hamada and Kohr is true in Banach spaces.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122518078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 20
Identities for the dirichlet integral of subharmonic functions from the cartright class 卡带类次调和函数狄利克雷积分的恒等式
Complex Variables, Theory and Application: An International Journal Pub Date : 2005-01-15 DOI: 10.1080/02781070412331328585
P. Kargaev, K. Evgeny
{"title":"Identities for the dirichlet integral of subharmonic functions from the cartright class","authors":"P. Kargaev, K. Evgeny","doi":"10.1080/02781070412331328585","DOIUrl":"https://doi.org/10.1080/02781070412331328585","url":null,"abstract":"Let a real function v be subharmonic in the plane and harmonic outside and . Assume that v belongs to the so-called subharmonic counterpart of the Cartright class of the entire functions. For such a function we obtain identities and estimates in terms of the Dirichlet integral.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125332012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
On the Douglas–Dirichlet functional and harmonic quasiconformal mappings 关于Douglas-Dirichlet泛函与调和拟共形映射
Complex Variables, Theory and Application: An International Journal Pub Date : 2004-12-15 DOI: 10.1080/02781070412331316920
Wei Han-bai
{"title":"On the Douglas–Dirichlet functional and harmonic quasiconformal mappings","authors":"Wei Han-bai","doi":"10.1080/02781070412331316920","DOIUrl":"https://doi.org/10.1080/02781070412331316920","url":null,"abstract":"In this article, we discuss the minimal mappings of Douglas–Dirichlet functional and harmonic quasiconformal mappings, and solve the uniqueness problem of harmonic quasiconformal mappings posed by Shibata.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132890112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Vector and operator-valued holomorphic functions representable by Carleman type formulas 由Carleman型公式表示的矢量和算子值全纯函数
Complex Variables, Theory and Application: An International Journal Pub Date : 2004-12-15 DOI: 10.1080/02781070412331327883
George Chailos
{"title":"Vector and operator-valued holomorphic functions representable by Carleman type formulas","authors":"George Chailos","doi":"10.1080/02781070412331327883","DOIUrl":"https://doi.org/10.1080/02781070412331327883","url":null,"abstract":"Let be a simply connected domain and let M be a connected subset of its boundary of positive Lebesque measure. With X we denote a separable Hilbert space or the space of bounded linear functionals on . We set f to be an X-valued holomorphic function, and with we denote the class of X-valued holomorphic functions on which belong to the Hardy class near the set M. In our main result, we show that if f belongs to , then f is representable by a Carleman type formula, and conversely, if f is representable by a Carleman type formula, and in some sense has an analytic continuation across M, then f belongs to . Furthermore we show that in general .","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124157323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Weighted value sharing and a question of I. Lahiri 加权价值共享与I. Lahiri问题
Complex Variables, Theory and Application: An International Journal Pub Date : 2004-12-15 DOI: 10.1080/02781070410001701074
T. Alzahary, Hong X. Yi †
{"title":"Weighted value sharing and a question of I. Lahiri","authors":"T. Alzahary, Hong X. Yi †","doi":"10.1080/02781070410001701074","DOIUrl":"https://doi.org/10.1080/02781070410001701074","url":null,"abstract":"In this article, we investigate the problem due to I. Lahiri [I. Lahiri (2001). Weighted value sharing and uniqueness of meromorphic functions. Complex Variables Theory Appl., 46, 241–253.]. Also we prove some uniqueness theorems of meromorphic functions which improve some earlier results.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"81 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120873639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 64
On the Fourier transform of distributions and differential operators in Clifford analysis Clifford分析中分布的傅里叶变换与微分算子
Complex Variables, Theory and Application: An International Journal Pub Date : 2004-12-15 DOI: 10.1080/02781070412331320457
Fred Brackx †, H. Schepper
{"title":"On the Fourier transform of distributions and differential operators in Clifford analysis","authors":"Fred Brackx †, H. Schepper","doi":"10.1080/02781070412331320457","DOIUrl":"https://doi.org/10.1080/02781070412331320457","url":null,"abstract":"In Brackx et al., 2004 (F. Brackx, R. Delanghe and F. Sommen (2004). Spherical means and distributions in Clifford analysis. In: Tao Qian, Thomas Hempfling, Alan McIntosch and Frank Sommen (Eds.), Advances in Analysis and Geometry: New Developments Using Clifford Algebra, Trends in Mathematics, pp. 65–96. Birkhäuser, Basel.), some fundamental higher dimensional distributions have been reconsidered within the framework of Clifford analysis. Here, the Fourier transforms of these distributions are calculated, revealing a.o. the Fourier symbols of some important translation invariant (convolution) operators, which can be interpreted as members of the considered families. Moreover, these results are the incentive for calculating the Fourier symbols of some differential operators which are at the heart of Clifford analysis, but do not show the property of translation invariance and hence, can no longer be interpreted as convolution operators.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116807868","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Rational decompositions of complex meromorphic functions 复亚纯函数的有理分解
Complex Variables, Theory and Application: An International Journal Pub Date : 2004-11-15 DOI: 10.1080/02781070412331310939
A. Escassut, Eberhard Mayerhofer †
{"title":"Rational decompositions of complex meromorphic functions","authors":"A. Escassut, Eberhard Mayerhofer †","doi":"10.1080/02781070412331310939","DOIUrl":"https://doi.org/10.1080/02781070412331310939","url":null,"abstract":"Let h be a complex meromorphic function. The problem of decomposing h in two different ways, P (f)  and Q(g) with f, g two other meromorphic functions and P, Q polynomials, was studied by C.-C. Yang, P. Li and H.K. Ha. Here we consider the problem when we replace the polynomials P, Q by rational functions F, G. Let deg(F ) be the maximum degree of numerator and denominator of F. Assume some zeros c 1, … ,c k of satisfy a pack of five conditions particularly involving G(d,) ≠ F(c j ) and D(d) ≠ 0 for every zero d of , with G = C/D,  (j = 1,…,k). First, we show that if f, g are entire functions such that F(f) = G(g), then k deg (G) ≤  deg(F). Now, let u be the number of distinct zeros of the denominator of G and assume that meromorphic functions f, g satisfy F(f) = G(g), then k deg (G) ≤  deg (F) + kγ (D). When zeros c 1, …, c k of satisfy a stronger condition, then we show that k deg (G) ≤  deg (F) + k min (γ (C), γ (D)). E-mail: eberhard.mayerhofer@univie.ac.at","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"26 6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126629281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Interpolating sequences for the fractral derivatives of Bloch functions in several variables 多变量Bloch函数分形导数的插值序列
Complex Variables, Theory and Application: An International Journal Pub Date : 2004-11-15 DOI: 10.1080/02781070412331298598
Shi Jihuai, L. Hua
{"title":"Interpolating sequences for the fractral derivatives of Bloch functions in several variables","authors":"Shi Jihuai, L. Hua","doi":"10.1080/02781070412331298598","DOIUrl":"https://doi.org/10.1080/02781070412331298598","url":null,"abstract":"In this paper, it is proved that the sufficiently separated sequences are interpolating sequences for when f is a Bloch function. In other words, for a sufficiently separated sequence {ak } and each bounded sequence {ck }, there exists at least one Bloch function f (z) such that .","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114104790","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sharp pointwise estimates for analytic functions by the L p -norm of the real part 用实部的L p范数对解析函数进行精确的点估计
Complex Variables, Theory and Application: An International Journal Pub Date : 2004-11-15 DOI: 10.1080/02781070412331298543
G. Kresin, V. Maz'ya
{"title":"Sharp pointwise estimates for analytic functions by the L p -norm of the real part","authors":"G. Kresin, V. Maz'ya","doi":"10.1080/02781070412331298543","DOIUrl":"https://doi.org/10.1080/02781070412331298543","url":null,"abstract":"We obtain sharp estimates of by the Lp -norm of on the circle , where , and α is a real valued function on DR . Here f is an analytic function in the disc whose real part is continuous on , ω is a real constant, and is orthogonal to some continuous function Φ on the circle . We derive two types of estimates with vanishing and nonvanishing mean value of Φ. The cases Φ = 0 and Φ = 1 are discussed in more detail. In particular, we give explicit formulas for sharp constants in inequalities for with p = 1, 2, ∞. We also obtain estimates for in the class of analytic functions with two-sided bounds of . As a corollary, we find a sharp constant in the upper estimate of by which generalizes the classical Carathéodory–Plemelj estimate with p=∞.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121310017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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