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

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On linear extremal problems in the class of schlicht functions schlicht函数类的线性极值问题
Complex Variables, Theory and Application: An International Journal Pub Date : 2005-11-01 DOI: 10.1080/02781070500277656
E. Michel
{"title":"On linear extremal problems in the class of schlicht functions","authors":"E. Michel","doi":"10.1080/02781070500277656","DOIUrl":"https://doi.org/10.1080/02781070500277656","url":null,"abstract":"The form of the Schiffer differential equation puts severe restrictions on the class of functions that can occur as extremal functions for arbitrary coefficient-functionals of finite degree. Theorem 1 characterizes the algebraic extremal functions for coefficient-functionals of finite degree. Furthermore it is shown that the extremal function either is an algebraic function or it must possess a non-isolated singularity, or must have a transcendental branch-point. The results are closely related to the Malmquist-Yosida theorems. However Nevanlinna's Theory of Value Distribution is not the mainly used tool but the special form of the Schiffer differential equation and the multiplicity of certain values together with the Great Picard Theorem are exploited.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125137429","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: 1
On a class of closed prime ideals in H ∞ H∞上的一类闭素数理想
Complex Variables, Theory and Application: An International Journal Pub Date : 2005-10-20 DOI: 10.1080/02781070500140524
K. Izuchi, Y. Izuchi
{"title":"On a class of closed prime ideals in H ∞","authors":"K. Izuchi, Y. Izuchi","doi":"10.1080/02781070500140524","DOIUrl":"https://doi.org/10.1080/02781070500140524","url":null,"abstract":"Gorkin and Mortini introduced the concept of k-hulls, k(x), of points x in M(H ∞) ∖ ∖D, and studied the ideal structures of H ∞ and H ∞ +C. They posed a problem for which x∈ M(H ∞) ∖ ∖D the set I(k(x)) is a closed prime ideal. In this article, we give a partial answer for sparse points x.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121566617","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
Characterization of holomorphic functions in terms of their moduli 全纯函数的模表征
Complex Variables, Theory and Application: An International Journal Pub Date : 2005-10-20 DOI: 10.1080/02781070500183086
H. Boche **, V. Pohl
{"title":"Characterization of holomorphic functions in terms of their moduli","authors":"H. Boche **, V. Pohl","doi":"10.1080/02781070500183086","DOIUrl":"https://doi.org/10.1080/02781070500183086","url":null,"abstract":"It was shown in (Boche, H. and Pohl, V., 2005, Spectral factorization in the disk algebra. Complex Variables. Theory and Applications, 50, 383–387.) that if the modulus |f| of a function is continuous in the closure of the unit disk, the function f itself needs not to be continuous there, in general. This article shows that if the modulus of continuity of a function is a weak regular majorant, the continuity of the modulus always implies the continuity of the function itself.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132609483","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: 8
Characterization of octonionic analytic functions 八元解析函数的表征
Complex Variables, Theory and Application: An International Journal Pub Date : 2005-10-20 DOI: 10.1080/02781070500230432
Xingmin Li, Zhao Kai, Lizhong Peng
{"title":"Characterization of octonionic analytic functions","authors":"Xingmin Li, Zhao Kai, Lizhong Peng","doi":"10.1080/02781070500230432","DOIUrl":"https://doi.org/10.1080/02781070500230432","url":null,"abstract":"It is shown that there is only one possible way to define the O-analytic functions. A simple way to construct the O-analytic functions is also given.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"123 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116124308","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: 28
Propagation of CR extendibility along complex tangent directions CR可拓性沿复切方向的传播
Complex Variables, Theory and Application: An International Journal Pub Date : 2005-10-10 DOI: 10.1080/02781070500156843
L. Baracco, G. Zampieri
{"title":"Propagation of CR extendibility along complex tangent directions","authors":"L. Baracco, G. Zampieri","doi":"10.1080/02781070500156843","DOIUrl":"https://doi.org/10.1080/02781070500156843","url":null,"abstract":"We discuss the propagation along CR curves of extendibility of CR functions in the framework of the theory of partial lifts of CR curves and of analytic discs introduced by the authors in (Baracco, L. and Zampieri, G., 2001, Analytic discs and extension of CR functions. Compositio Mathematica, 127, 289–295) and (Baracco, L. and Zampieri, G., 2002, Tangent discs and extension of CR functions to wedges of . J. Geom. Analysis, 12(1), 1–7).","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127343055","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
On order of convexity of functions defined by certain integral transforms 关于由某些积分变换定义的函数的凸性
Complex Variables, Theory and Application: An International Journal Pub Date : 2005-10-10 DOI: 10.1080/02781070500032812
M. Anbu Durai, R. Parvatham
{"title":"On order of convexity of functions defined by certain integral transforms","authors":"M. Anbu Durai, R. Parvatham","doi":"10.1080/02781070500032812","DOIUrl":"https://doi.org/10.1080/02781070500032812","url":null,"abstract":"For real-valued, monotonically decreasing on [0, 1] satisfying the conditions as t→0+ and increasing on (0, 1), we obtain that for a suitable f (z), where Using this result we obtain several other general results. We determine the least value of β so that for g analytic in and for the functions and are convex of order γ. Here 2F 1 is the Gaussian hypergeometric function. We have extended these results to functions of the form Corresponding starlikeness result is obtained for such convex combinations.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131555850","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: 1
Dirichlet problems for generalized Cauchy–Riemann systems with singular coefficients 广义Cauchy-Riemann系统的Dirichlet问题
Complex Variables, Theory and Application: An International Journal Pub Date : 2005-06-10 DOI: 10.1080/02781070500087196
M. Reissig, A. Timofeev
{"title":"Dirichlet problems for generalized Cauchy–Riemann systems with singular coefficients","authors":"M. Reissig, A. Timofeev","doi":"10.1080/02781070500087196","DOIUrl":"https://doi.org/10.1080/02781070500087196","url":null,"abstract":"The article is devoted to the Dirichlet problem in the unit disk G for on ∂, Im w = h in z 0 = 1, where g is a given Hölder continuous function. The coefficient b belongs to a subspace of L 2(G) which is in general not contained in Lq(G), q > 2. Thus Vekua's theory is not applicable. Nevertheless we are able to prove the uniqueness of continuous solutions in .","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131485605","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: 7
Discontinuous Riemann–Hilbert problems for quasilinear degenerate elliptic complex equations of first order 拟线性退化椭圆型一阶复方程的不连续Riemann-Hilbert问题
Complex Variables, Theory and Application: An International Journal Pub Date : 2005-06-10 DOI: 10.1080/02781070500087626
G. Wen, Dechang Chen
{"title":"Discontinuous Riemann–Hilbert problems for quasilinear degenerate elliptic complex equations of first order","authors":"G. Wen, Dechang Chen","doi":"10.1080/02781070500087626","DOIUrl":"https://doi.org/10.1080/02781070500087626","url":null,"abstract":"In this article we discuss discontinuous Riemann–Hilbert problems for quasilinear degenerate elliptic systems of first order equations in a bounded simply connected domain. Firstly the representation of solutions of the boundary value problems for the equations is given, and then the existence and uniqueness of solutions for the problems are proved.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"319 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133339619","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: 8
On a Nevanlinna type result for solutions of nonautonomous equations y′=a( t) F 1( x,y), x′=b( t)F 2( x,y ) 非自治方程y ' =a(t) f1 (x,y)， x ' =b(t) f2 (x,y)解的Nevanlinna型结果
Complex Variables, Theory and Application: An International Journal Pub Date : 2005-06-10 DOI: 10.1080/02781070500086438
K. Barseghyan, G. Barsegian
{"title":"On a Nevanlinna type result for solutions of nonautonomous equations y′=a( t) F 1( x,y), x′=b( t)F 2( x,y )","authors":"K. Barseghyan, G. Barsegian","doi":"10.1080/02781070500086438","DOIUrl":"https://doi.org/10.1080/02781070500086438","url":null,"abstract":"Oscillation problems (investigation of zeros) were widely studied for solutions of ordinary differential equation (ODE). In this article, we transfer oscillation problems to the case of solutions of nonautonomous system of equations . By analogy with the theory of oscillation for one ODE, we consider number n(t 1,t 2,0) of zeros τ i in (t 1,t 2) of the solutions, that is the number of those points τ i , where x(τ i ) =0 and y(τ i )=0. It turns out that the above bounds for n(t 1,t 2,0) can be given in terms of a( t) , b( t) , F 1, F 2, t 1 and t 2. Also by analogy with the concept of a-points in the complex analysis, we consider values a:=(a′,a″) in the ( x, y )-plane and define a-points of the solutions as those points τ i , where and . Denoting by n(t 1,t 2, a) the number of a-points in (t 1,t 2) of the solutions we give above bounds for the sum , where a 1,a 2,…,aq is a given totality of pairwise different points. Thus we obtain for the solutions of the above equation an analog of the second fundamental theorem in the Nevanlinna value distribution theory; the last one also considers a similar sum for the number of a-points of meromorphic functions. As an immediate application we obtain below bounds for the periods of periodic solutions.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"2894 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126997617","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
Professor Dr. Heinrich Begehr 亨利教授
Complex Variables, Theory and Application: An International Journal Pub Date : 2005-06-10 DOI: 10.1080/02781070512331389541
H. Begehr
{"title":"Professor Dr. Heinrich Begehr","authors":"H. Begehr","doi":"10.1080/02781070512331389541","DOIUrl":"https://doi.org/10.1080/02781070512331389541","url":null,"abstract":"","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130764200","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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