Pub Date : 2005-05-15DOI: 10.1080/02781070500140532
Toshihide Futamura, Y. Mizuta
This article deals with weighted boundary limits of monotone Sobolev functions on bounded s-John domains in a metric space.
本文研究了度量空间中有界s-John区域上单调Sobolev函数的加权边界极限。
{"title":"Boundary behavior of monotone Sobolev functions on John domains in a metric space","authors":"Toshihide Futamura, Y. Mizuta","doi":"10.1080/02781070500140532","DOIUrl":"https://doi.org/10.1080/02781070500140532","url":null,"abstract":"This article deals with weighted boundary limits of monotone Sobolev functions on bounded s-John domains in a metric space.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125568668","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 : 2005-05-15DOI: 10.1080/02781070500140573
S. Krantz
In this article, we give new, elementary, and very geometric proofs of two results in conformal mapping theory. One of these – about the size of the isotropy group of the set of conformal mappings of a domain – is nearly three-quarters of a century old. The other – about fixed points – is just two decades old.
{"title":"Two results on uniqueness of conformal mappings","authors":"S. Krantz","doi":"10.1080/02781070500140573","DOIUrl":"https://doi.org/10.1080/02781070500140573","url":null,"abstract":"In this article, we give new, elementary, and very geometric proofs of two results in conformal mapping theory. One of these – about the size of the isotropy group of the set of conformal mappings of a domain – is nearly three-quarters of a century old. The other – about fixed points – is just two decades old.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124028815","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 : 2005-05-15DOI: 10.1080/02781070500044460
H. Boche **, V. Pohl
Every strictly positive function f, given on the unit circle of the complex plane, defines an outer function. This article investigates the behavior of these outer functions on the boundary of the unit disk. It is shown that even if the given function f on the boundary is continuous, the corresponding outer function is generally not continuous on the closure of the unit disk. Moreover, any subset E∈ [-π ,π) of Lebesgue measure zero is a valid divergence set for outer functions of some continuous functions f. These results are applied to study the solutions of non-linear boundary-value problems and the factorization of spectral density functions.
{"title":"Spectral factorization in the disk algebra","authors":"H. Boche **, V. Pohl","doi":"10.1080/02781070500044460","DOIUrl":"https://doi.org/10.1080/02781070500044460","url":null,"abstract":"Every strictly positive function f, given on the unit circle of the complex plane, defines an outer function. This article investigates the behavior of these outer functions on the boundary of the unit disk. It is shown that even if the given function f on the boundary is continuous, the corresponding outer function is generally not continuous on the closure of the unit disk. Moreover, any subset E∈ [-π ,π) of Lebesgue measure zero is a valid divergence set for outer functions of some continuous functions f. These results are applied to study the solutions of non-linear boundary-value problems and the factorization of spectral density functions.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"400 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114927268","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 : 2005-05-15DOI: 10.1080/02781070500139807
R. Hidalgo
A real algebraic curve of genus g is a pair (S,τ), where S is a closed Riemann surface of genus g and τ :S → S is an anticonformal involution. It was already known to Koebe that each real algebraic curve for which τ is a reflection can be uniformized by a real Schottky group, that is, a Schottky group that keeps invariant the unit circle. In the case that τ is an imaginary reflection, we produce uniformizations by either (i) real noded Klein–Schottky groups (once we have chosen some points on S as phantom nodes) or (ii) Klein–Schottky groups. We also give explicit descriptions of the real algebraic curves of genus 2 in terms of these types of uniformizing groups.
{"title":"Real Schottky parametrizations","authors":"R. Hidalgo","doi":"10.1080/02781070500139807","DOIUrl":"https://doi.org/10.1080/02781070500139807","url":null,"abstract":"A real algebraic curve of genus g is a pair (S,τ), where S is a closed Riemann surface of genus g and τ :S → S is an anticonformal involution. It was already known to Koebe that each real algebraic curve for which τ is a reflection can be uniformized by a real Schottky group, that is, a Schottky group that keeps invariant the unit circle. In the case that τ is an imaginary reflection, we produce uniformizations by either (i) real noded Klein–Schottky groups (once we have chosen some points on S as phantom nodes) or (ii) Klein–Schottky groups. We also give explicit descriptions of the real algebraic curves of genus 2 in terms of these types of uniformizing groups.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"120 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124743651","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 : 2005-05-15DOI: 10.1080/02781070500132679
F. Colombo, A. Damiano, I. Sabadini, D. Struppa
In this article we show that it is possible to construct a Koszul-type complex for maps given by suitable pairwise commuting matrices of polynomials. This result has applications to surjectivity theorems for constant coefficients differential operators of finite and infinite order. In particular, we construct a large class of constant coefficients differential operators which are surjective on the space of regular (or monogenic) functions on open convex sets.
{"title":"A surjectivity theorem for differential operators on spaces of regular functions","authors":"F. Colombo, A. Damiano, I. Sabadini, D. Struppa","doi":"10.1080/02781070500132679","DOIUrl":"https://doi.org/10.1080/02781070500132679","url":null,"abstract":"In this article we show that it is possible to construct a Koszul-type complex for maps given by suitable pairwise commuting matrices of polynomials. This result has applications to surjectivity theorems for constant coefficients differential operators of finite and infinite order. In particular, we construct a large class of constant coefficients differential operators which are surjective on the space of regular (or monogenic) functions on open convex sets.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121642719","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 : 2005-04-15DOI: 10.1080/02781070500032895
J. Konderak
We consider functions with values in the algebra of Lorentz numbers which are differentiable with respect to the algebraic structure of as an analogue of holomorphic functions. Then we apply these functions to prove a Weierstrass representation theorem for Lorentz surfaces immersed in the space . In the proof we essentially follow the model of the complex numbers. We apply our representation theorem to construct explicit minimal immersions.
{"title":"A Weierstrass representation theorem for Lorentz surfaces","authors":"J. Konderak","doi":"10.1080/02781070500032895","DOIUrl":"https://doi.org/10.1080/02781070500032895","url":null,"abstract":"We consider functions with values in the algebra of Lorentz numbers which are differentiable with respect to the algebraic structure of as an analogue of holomorphic functions. Then we apply these functions to prove a Weierstrass representation theorem for Lorentz surfaces immersed in the space . In the proof we essentially follow the model of the complex numbers. We apply our representation theorem to construct explicit minimal immersions.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"160 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129966887","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 : 2005-04-15DOI: 10.1080/02781070500128354
Mehmet Sezer, Mustafa Gülsu
In this article, a Taylor matrix method is developed to find an approximate solution of the most general linear Fredholm integrodifferential–difference equations with variable coefficients under the mixed conditions in terms of Taylor polynomials. Also numerical examples are presented, which illustrate the pertinent features of the method. In some numerical examples, MAPLE modules are designed for the purpose of testing and using the method.
{"title":"Polynomial solution of the most general linear Fredholm integrodifferential–difference equations by means of Taylor matrix method","authors":"Mehmet Sezer, Mustafa Gülsu","doi":"10.1080/02781070500128354","DOIUrl":"https://doi.org/10.1080/02781070500128354","url":null,"abstract":"In this article, a Taylor matrix method is developed to find an approximate solution of the most general linear Fredholm integrodifferential–difference equations with variable coefficients under the mixed conditions in terms of Taylor polynomials. Also numerical examples are presented, which illustrate the pertinent features of the method. In some numerical examples, MAPLE modules are designed for the purpose of testing and using the method.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130775441","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 : 2005-04-15DOI: 10.1080/02781070500032879
G. Barsegian, D. Le
In this article we give a topological approach to the global behavior of arbitrary single-valued solutions in a simple connected domain of some general classes of complex differential equations with multi-valued coefficients. In particular, this permits us to describe certain globally multi-valued solutions as well as algebraic and algebroid solutions.
{"title":"On a topological description of solutions of complex differential equations","authors":"G. Barsegian, D. Le","doi":"10.1080/02781070500032879","DOIUrl":"https://doi.org/10.1080/02781070500032879","url":null,"abstract":"In this article we give a topological approach to the global behavior of arbitrary single-valued solutions in a simple connected domain of some general classes of complex differential equations with multi-valued coefficients. In particular, this permits us to describe certain globally multi-valued solutions as well as algebraic and algebroid solutions.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121803244","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 : 2005-04-15DOI: 10.1080/02781070500032788
Li Songxiao, Zhuang Xiangling
This article provides information on p-logarithmic s-Carleson measure characterization of the weighted BMOA spaces. Also, the boundedness and compactness of composition operators from Bloch-type space and weighted Bloch space to weighted BMOA space are discussed.
{"title":"Weighted BMOA spaces and composition operators","authors":"Li Songxiao, Zhuang Xiangling","doi":"10.1080/02781070500032788","DOIUrl":"https://doi.org/10.1080/02781070500032788","url":null,"abstract":"This article provides information on p-logarithmic s-Carleson measure characterization of the weighted BMOA spaces. Also, the boundedness and compactness of composition operators from Bloch-type space and weighted Bloch space to weighted BMOA space are discussed.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116642109","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 : 2005-04-15DOI: 10.1080/02781070500087766
V. K. Jain
According to Grace's apolarity theorem, if the coefficient of two polynomials satisfy the equation then (i) f(z) has at least one zero, in a circular region C containing all zeros of g(z) (ii) g(z) has at least one zero, in a circular region C containing all zeros of f(z). We have obtained generalizations of (i), by considering g(z) to be any polynomial of degree not exceeding n and C to be a circular region (containing 0) or a circular region with a convex complement and generalizations of (ii), by considering g(z) to be any polynomial of degree not exceeding n and C to be a circular region (not containing 0) or a convex circular region. We have applied these generalizations to the study of the zeros of certain composite polynomials (obtained from two given polynomials), thereby leading also to certain generalizations of Szegö's theorem [Szegö, G., 1922, Bemerkungen zu einem Satz von J.H. Grace über die Wurzeln algebraischer Gleichungen. Mathematische Zeitschrift, 13, 28–55.] involving circular regions (with a characteristic).
根据Grace的极性定理，如果两个多项式的系数满足方程，则(i) f(z)在包含g(z)的所有零的圆形区域C中至少有一个零;(ii) g(z)在包含f(z)的所有零的圆形区域C中至少有一个零。通过考虑g(z)为不超过n次的多项式，C为不超过n次的圆区域(含0)或带凸补的圆区域，我们得到了(i)的推广;通过考虑g(z)为不超过n次的多项式，C为不超过0次的圆区域(含0)或凸圆区域，我们得到了(ii)的推广。我们已经将这些推广应用于某些复合多项式(由两个给定多项式得到)的零点的研究，从而也导致Szegö定理的某些推广[Szegö， G.， 1922, Bemerkungen zu einem Satz von J.H. Grace ber die Wurzeln algebraischer Gleichungen]。数学时代，13,28-55。涉及圆形区域的(有特征的)。
{"title":"Generalizations of parts of Grace's apolarity theorem involving circular regions (with a characteristic) and their applications","authors":"V. K. Jain","doi":"10.1080/02781070500087766","DOIUrl":"https://doi.org/10.1080/02781070500087766","url":null,"abstract":"According to Grace's apolarity theorem, if the coefficient of two polynomials satisfy the equation then (i) f(z) has at least one zero, in a circular region C containing all zeros of g(z) (ii) g(z) has at least one zero, in a circular region C containing all zeros of f(z). We have obtained generalizations of (i), by considering g(z) to be any polynomial of degree not exceeding n and C to be a circular region (containing 0) or a circular region with a convex complement and generalizations of (ii), by considering g(z) to be any polynomial of degree not exceeding n and C to be a circular region (not containing 0) or a convex circular region. We have applied these generalizations to the study of the zeros of certain composite polynomials (obtained from two given polynomials), thereby leading also to certain generalizations of Szegö's theorem [Szegö, G., 1922, Bemerkungen zu einem Satz von J.H. Grace über die Wurzeln algebraischer Gleichungen. Mathematische Zeitschrift, 13, 28–55.] involving circular regions (with a characteristic).","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130839369","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}
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