Pub Date : 2004-05-15DOI: 10.1080/02781070410001712702
Peter Hästö *, Henri Lindén
The half-Apollonian metric is a generalization of the hyperbolic metric, similar to the Apollonian metric. It can be defined in arbitrary domains in the euclidean space and has the advantages of being easy to calculate and estimate. We show that the half-Apollonian metric has many geodesics and use this fact to show that in most domains all the isometries of the metric are similarity mappings.
{"title":"Isometries of the Half-Apollonian Metric","authors":"Peter Hästö *, Henri Lindén","doi":"10.1080/02781070410001712702","DOIUrl":"https://doi.org/10.1080/02781070410001712702","url":null,"abstract":"The half-Apollonian metric is a generalization of the hyperbolic metric, similar to the Apollonian metric. It can be defined in arbitrary domains in the euclidean space and has the advantages of being easy to calculate and estimate. We show that the half-Apollonian metric has many geodesics and use this fact to show that in most domains all the isometries of the metric are similarity mappings.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125004201","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 : 2004-05-15DOI: 10.1080/02781070410001715097
A. Singh, Ajaya Singh †
Some criteria for determining the normality of the family of meromorphic functions in the unit disc, which share values depending on with their derivatives is obtained.
给出了单位圆盘上亚纯函数族正态性的判定准则，这些亚纯函数族的共享值依赖于它们的导数。
{"title":"Sharing Values and Normality of Meromorphic Functions","authors":"A. Singh, Ajaya Singh †","doi":"10.1080/02781070410001715097","DOIUrl":"https://doi.org/10.1080/02781070410001715097","url":null,"abstract":"Some criteria for determining the normality of the family of meromorphic functions in the unit disc, which share values depending on with their derivatives is obtained.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114927348","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 : 2004-05-15DOI: 10.1080/0278107042000220276
A. Pogorui *, M. Shapiro
We prove that any quaternionic polynomial (with the coefficients on the same side) has two types of zeroes: the zeroes are either isolated or spherical ones, i.e., those ones which form a whole sphere. What is more, the total quantity of the isolated zeroes and of the double number of the spheres does not outnumber the degree of the polynomial.
{"title":"On the Structure of the Set of Zeros of Quaternionic Polynomials","authors":"A. Pogorui *, M. Shapiro","doi":"10.1080/0278107042000220276","DOIUrl":"https://doi.org/10.1080/0278107042000220276","url":null,"abstract":"We prove that any quaternionic polynomial (with the coefficients on the same side) has two types of zeroes: the zeroes are either isolated or spherical ones, i.e., those ones which form a whole sphere. What is more, the total quantity of the isolated zeroes and of the double number of the spheres does not outnumber the degree of the polynomial.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122498359","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 : 2004-05-15DOI: 10.1080/0278107040001717149
Sezayi Hizliyel, Mehmet Ça[gtilde]liyan †
In this work, we will develop a Vekua-type theory for the equation where Q = (q ij (z)) is a self-commuting complex matrix with m × m and for k = 2, …,m. A and B commuting with Q, which is
{"title":"Generalized Q-Holomorphic Functions","authors":"Sezayi Hizliyel, Mehmet Ça[gtilde]liyan †","doi":"10.1080/0278107040001717149","DOIUrl":"https://doi.org/10.1080/0278107040001717149","url":null,"abstract":"In this work, we will develop a Vekua-type theory for the equation where Q = (q ij (z)) is a self-commuting complex matrix with m × m and for k = 2, …,m. A and B commuting with Q, which is","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"106 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123684020","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 : 2004-04-15DOI: 10.1080/02781070410001710344
Wael Bahsoun, Pawel Góra †
We discuss exactness and dissipative behavior of inner functions with ∞ as the Denjoy–Wolff point. We give an example of an inner function g which preserves Lebesgue measure on with and g(x) being (totally) dissipative on J(g). E-mail: pgora@vax2.concordia.ca
{"title":"Dissipative and exact inner functions","authors":"Wael Bahsoun, Pawel Góra †","doi":"10.1080/02781070410001710344","DOIUrl":"https://doi.org/10.1080/02781070410001710344","url":null,"abstract":"We discuss exactness and dissipative behavior of inner functions with ∞ as the Denjoy–Wolff point. We give an example of an inner function g which preserves Lebesgue measure on with and g(x) being (totally) dissipative on J(g). E-mail: pgora@vax2.concordia.ca","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129884266","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 : 2004-04-15DOI: 10.1080/02781070410001713044
S. M. Elzaidi
Suppose A and B are entire functions. We assume that A is transcendental. If either the order of B is less than the order of A and the order of A is less than 1/2, or the order of A is zero and B is a polynomial, it is shown that every nonconstant solution of the differential equation has infinitely many zeros.
{"title":"On the oscillation of solutions of the differential equation y″′ + Ay′ + By = 0","authors":"S. M. Elzaidi","doi":"10.1080/02781070410001713044","DOIUrl":"https://doi.org/10.1080/02781070410001713044","url":null,"abstract":"Suppose A and B are entire functions. We assume that A is transcendental. If either the order of B is less than the order of A and the order of A is less than 1/2, or the order of A is zero and B is a polynomial, it is shown that every nonconstant solution of the differential equation has infinitely many zeros.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115179089","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 : 2004-04-15DOI: 10.1080/0278107041000179038
Y. Gong, Jinyuan Du †
In this article, some properties of Cauchy-type integral and singular integral with integration domain are discussed, especially their boundary value properties at ∞. With the help of Painlevé theorem and Liouville theorem, a Riemann Boundary Value Problem (BVP for short) and a Hilbert BVP for left monogenic functions in Clifford analysis are investigated in the classical sense, their explicit representation of solutions are obtained respectively.
{"title":"A kind of Riemann and Hilbert boundary value problem for left monogenic functions in Rm (m ≥ 2)","authors":"Y. Gong, Jinyuan Du †","doi":"10.1080/0278107041000179038","DOIUrl":"https://doi.org/10.1080/0278107041000179038","url":null,"abstract":"In this article, some properties of Cauchy-type integral and singular integral with integration domain are discussed, especially their boundary value properties at ∞. With the help of Painlevé theorem and Liouville theorem, a Riemann Boundary Value Problem (BVP for short) and a Hilbert BVP for left monogenic functions in Clifford analysis are investigated in the classical sense, their explicit representation of solutions are obtained respectively.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133776380","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 : 2004-04-15DOI: 10.1080/02781070410001710353
N. Hayashi, Pavel I. Naumkin †
We consider the Cauchy problem for the cubic nonlinear Schrödinger equation where We prove the global existence of small solutions , if the initial data u 1 belong to some analytic function space and are sufficiently small. For the coefficients λ j we assume that there exists θ 0 > 0 such that for all and also we suppose that the initial data are such that where ϵ is a small positive constant depending on the size of initial function in a suitable norm. We also find the large time asymptotic formulas for solutions. In the short range region the solution has an additional logarithmic time decay comparing with the corresponding linear case.
{"title":"On the asymptotics for cubic nonlinear Schrödinger equations","authors":"N. Hayashi, Pavel I. Naumkin †","doi":"10.1080/02781070410001710353","DOIUrl":"https://doi.org/10.1080/02781070410001710353","url":null,"abstract":"We consider the Cauchy problem for the cubic nonlinear Schrödinger equation where We prove the global existence of small solutions , if the initial data u 1 belong to some analytic function space and are sufficiently small. For the coefficients λ j we assume that there exists θ 0 > 0 such that for all and also we suppose that the initial data are such that where ϵ is a small positive constant depending on the size of initial function in a suitable norm. We also find the large time asymptotic formulas for solutions. In the short range region the solution has an additional logarithmic time decay comparing with the corresponding linear case.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"187 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114308862","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 : 2004-04-15DOI: 10.1080/02781070410001702541
T. Nakazi
We are interested in extremal functions in a Hardy space . For example, we study extreme points of the unit ball of H 1(Tn ) and give a factorization theorem. In particular, we show that any rational function can be factorized.
{"title":"Factorizations of functions in Hp (Tn )","authors":"T. Nakazi","doi":"10.1080/02781070410001702541","DOIUrl":"https://doi.org/10.1080/02781070410001702541","url":null,"abstract":"We are interested in extremal functions in a Hardy space . For example, we study extreme points of the unit ball of H 1(Tn ) and give a factorization theorem. In particular, we show that any rational function can be factorized.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115173484","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 : 2004-04-15DOI: 10.1080/02781070410001701047
E. Ballico
Let X be a topological space whose topology may be defined by a complete metric d. Taking all such metrics d we define a universal complex structure on X. For this complex structure the sheaf of germs of holomorphic functions on X coincides with the sheaf of germs of continuous functions on X, and hence the theories of topological and holomorphic vector bundles on X are the same.
{"title":"A universal complex structure on complete metrizable topological spaces","authors":"E. Ballico","doi":"10.1080/02781070410001701047","DOIUrl":"https://doi.org/10.1080/02781070410001701047","url":null,"abstract":"Let X be a topological space whose topology may be defined by a complete metric d. Taking all such metrics d we define a universal complex structure on X. For this complex structure the sheaf of germs of holomorphic functions on X coincides with the sheaf of germs of continuous functions on X, and hence the theories of topological and holomorphic vector bundles on X are the same.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116872681","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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