Pub Date : 2005-11-01DOI: 10.1080/02781070500277656
E. Michel
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.
{"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}
Pub Date : 2005-10-20DOI: 10.1080/02781070500140524
K. Izuchi, Y. Izuchi
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.
{"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}
Pub Date : 2005-10-20DOI: 10.1080/02781070500183086
H. Boche **, V. Pohl
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.
在(Boche, H. and Pohl, V.， 2005)，《磁盘代数中的谱分解》中得到了证明。复杂的变量。理论与应用，50,383-387 .)，如果函数的模f在单位圆盘的闭包中是连续的，则函数f本身在那里一般不必是连续的。本文证明了如果一个函数的连续模是弱正则主量，则该模的连续性总是隐含着函数本身的连续性。
{"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}
Pub Date : 2005-10-20DOI: 10.1080/02781070500230432
Xingmin Li, Zhao Kai, Lizhong Peng
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.
证明了定义o解析函数只有一种可能的方法。给出了构造o解析函数的一种简单方法。
{"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}
Pub Date : 2005-10-10DOI: 10.1080/02781070500156843
L. Baracco, G. Zampieri
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).
本文在Baracco, L. and Zampieri, G.， 2001《解析盘与CR函数的可拓》一文中介绍的CR曲线和解析盘的部分提升理论的框架下，讨论了CR函数的可拓性在CR曲线上的传播。Baracco, L.和Zampieri, G.， 2002，切线圆盘和CR函数在楔形的推广。j .几何学。分析，12(1)，1 - 7。
{"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}
Pub Date : 2005-10-10DOI: 10.1080/02781070500032812
M. Anbu Durai, R. Parvatham
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.
{"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}
Pub Date : 2005-06-10DOI: 10.1080/02781070500087196
M. Reissig, A. Timofeev
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 .
本文致力于在∂，Im w = h in z 0 = 1的单位磁盘G中的Dirichlet问题，其中G是一个给定的Hölder连续函数。系数b属于l2 (G)的一个子空间，一般不包含在Lq(G)中，q > 2。因此，Vekua的理论并不适用。然而，我们能够证明连续解的唯一性。
{"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}
Pub Date : 2005-06-10DOI: 10.1080/02781070500087626
G. Wen, Dechang Chen
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.
{"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}
Pub Date : 2005-06-10DOI: 10.1080/02781070500086438
K. Barseghyan, G. Barsegian
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.
{"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}
Pub Date : 2005-06-10DOI: 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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：