Pub Date : 2004-06-10DOI: 10.1080/0278107041001732160
O. Martio, V. Miklyukov
Existence and uniqueness of solutions of degenerate Beltrami equation are studied under the condition that the dilatation K has an upper bound in W 1,2.
研究了简并Beltrami方程在扩张K在w1,2上有上界的条件下解的存在唯一性。
{"title":"On existence and uniqueness of degenerate beltrami equation","authors":"O. Martio, V. Miklyukov","doi":"10.1080/0278107041001732160","DOIUrl":"https://doi.org/10.1080/0278107041001732160","url":null,"abstract":"Existence and uniqueness of solutions of degenerate Beltrami equation are studied under the condition that the dilatation K has an upper bound in W 1,2.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121413124","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 : 2004-06-10DOI: 10.1080/02781070410001732142
J. Langley, J. Rossi
We prove some results on critical points of potentials arising from discrete distributions of charge in the plane and in space, and on zeros of certain associated meromorphic functions.
我们证明了平面和空间中电荷离散分布所引起的势的临界点，以及某些相关亚纯函数的零点上的一些结果。
{"title":"Critical points of certain discrete potentials","authors":"J. Langley, J. Rossi","doi":"10.1080/02781070410001732142","DOIUrl":"https://doi.org/10.1080/02781070410001732142","url":null,"abstract":"We prove some results on critical points of potentials arising from discrete distributions of charge in the plane and in space, and on zeros of certain associated meromorphic functions.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122683585","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 : 2004-06-10DOI: 10.1080/02781070410001731648
Carlos Berenstein a, Der-Chen Chang b, W. Eby
The goal of the paper is to verify Hörmander's strongly coprime condition for two Bessel functions (of the first kind), adjusted not to vanish at zero, whose indices have a certain relationship. These Bessel functions, and , must have indices which differ by a positive integer, i.e., , and the index . As a consequence of satisfying Hörmander's condition, these two functions are then known to generate (algebraically) the space of Fourier transforms of the space , by means of writing The results are also applied to radial functions in R n .
{"title":"A Note on Hörmander's strongly coprime condition","authors":"Carlos Berenstein a, Der-Chen Chang b, W. Eby","doi":"10.1080/02781070410001731648","DOIUrl":"https://doi.org/10.1080/02781070410001731648","url":null,"abstract":"The goal of the paper is to verify Hörmander's strongly coprime condition for two Bessel functions (of the first kind), adjusted not to vanish at zero, whose indices have a certain relationship. These Bessel functions, and , must have indices which differ by a positive integer, i.e., , and the index . As a consequence of satisfying Hörmander's condition, these two functions are then known to generate (algebraically) the space of Fourier transforms of the space , by means of writing The results are also applied to radial functions in R n .","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"130 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127098274","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 : 2004-06-10DOI: 10.1080/02781070412331272514
W. Hayman
Complex Analysts have suffered a severe loss with the departure of Matts Essén. When we celebrated him on the occasion of his retirement in June 1997, he was at the height of his powers. At that time I gave an interim report and was confident that he would greatly add to his achievements in the years to come. Alas he only had 6 years to do it in, but even so he fully justified my prediction. Several mathematicians will express their appreciation of Matts in this volume, but many more will miss a great and generous friend. Sten Kaijser in his fine Biography of Matts has pointed out the remarkable fact that 60% of Matts’ Mathematical papers were published after his 50th birthday. This is a great encouragement to the rest of us, especially when our friends tell us that Mathematicians are all genuises at 20 and after that it is downhill all the way. It seems to me that the reason why Matts was such a good counterexample to this theory was that he was such a great collaborator and friend. He was really interested in what we were doing, he listened and thought about it and could often bring out the sparkling diamond from the uncut stone. The same quality made him such a good companion. He loved to sing, play the piano, swim and ski with us. Conferences were not the same without him and Agneta. I remember their arriving at our Canterbury conference in 1973. Agneta told me then how much she had enjoyed the Meeting and that she wanted to come to many more such Meetings! It was because they both enjoyed these occasions that they were able to contribute so much to their success. Matts could not have been so good a host and friend without the marvellous qualities that Agneta contributed to the marriage. Of course Matts was a fine pianist, but Agneta is the only wife I know who actually claimed to enjoy listening to her husband’s playing. My wives were always pleased when I stopped! Agneta has a deep appreciation of literature and the arts. She introduced me to Strindberg and she and Matts invited me to an enchanting evening at Drottningholm. It was always wonderful to be with them. Many Mathematicians from all over the world were entertained by Matts and Agneta and left their hospitable home refreshed and full of good food and good ideas. In conclusion I would like to highlight a few results of Matts that I could not refer to in 1997. Let me start with [87-6].
{"title":"A Tribute to Matts Essén","authors":"W. Hayman","doi":"10.1080/02781070412331272514","DOIUrl":"https://doi.org/10.1080/02781070412331272514","url":null,"abstract":"Complex Analysts have suffered a severe loss with the departure of Matts Essén. When we celebrated him on the occasion of his retirement in June 1997, he was at the height of his powers. At that time I gave an interim report and was confident that he would greatly add to his achievements in the years to come. Alas he only had 6 years to do it in, but even so he fully justified my prediction. Several mathematicians will express their appreciation of Matts in this volume, but many more will miss a great and generous friend. Sten Kaijser in his fine Biography of Matts has pointed out the remarkable fact that 60% of Matts’ Mathematical papers were published after his 50th birthday. This is a great encouragement to the rest of us, especially when our friends tell us that Mathematicians are all genuises at 20 and after that it is downhill all the way. It seems to me that the reason why Matts was such a good counterexample to this theory was that he was such a great collaborator and friend. He was really interested in what we were doing, he listened and thought about it and could often bring out the sparkling diamond from the uncut stone. The same quality made him such a good companion. He loved to sing, play the piano, swim and ski with us. Conferences were not the same without him and Agneta. I remember their arriving at our Canterbury conference in 1973. Agneta told me then how much she had enjoyed the Meeting and that she wanted to come to many more such Meetings! It was because they both enjoyed these occasions that they were able to contribute so much to their success. Matts could not have been so good a host and friend without the marvellous qualities that Agneta contributed to the marriage. Of course Matts was a fine pianist, but Agneta is the only wife I know who actually claimed to enjoy listening to her husband’s playing. My wives were always pleased when I stopped! Agneta has a deep appreciation of literature and the arts. She introduced me to Strindberg and she and Matts invited me to an enchanting evening at Drottningholm. It was always wonderful to be with them. Many Mathematicians from all over the world were entertained by Matts and Agneta and left their hospitable home refreshed and full of good food and good ideas. In conclusion I would like to highlight a few results of Matts that I could not refer to in 1997. Let me start with [87-6].","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133818246","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 : 2004-06-10DOI: 10.1080/02781070410001731729
C. Bandle, M. Marcus
Let D be a smooth bounded domain in . Let f be a positive monotone increasing function on which satisfies the Keller–Osserman condition. It is well-known that the solutions of Δ u=f(u), which blow up at the boundary behave, to a first order approximation, like a function of dist(x,∂ D). In this paper we show that the second order approximation depends on the mean curvature of ∂ D. This paper is an extension of results in [4] which dealt with radially symmetric solutions. It extends also the results in [5] for f = tp .
{"title":"Dependence of blowup rate of large solutions of semilinear elliptic equations, on the curvature of the boundary","authors":"C. Bandle, M. Marcus","doi":"10.1080/02781070410001731729","DOIUrl":"https://doi.org/10.1080/02781070410001731729","url":null,"abstract":"Let D be a smooth bounded domain in . Let f be a positive monotone increasing function on which satisfies the Keller–Osserman condition. It is well-known that the solutions of Δ u=f(u), which blow up at the boundary behave, to a first order approximation, like a function of dist(x,∂ D). In this paper we show that the second order approximation depends on the mean curvature of ∂ D. This paper is an extension of results in [4] which dealt with radially symmetric solutions. It extends also the results in [5] for f = tp .","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125169538","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 : 2004-06-10DOI: 10.1080/02781070410001731701
K. Ishizaki, Niro Yanagihara ‡
Eremenko and Sodin proved that meromorphic solution f (z) of the Schröder equation f (sz) = R (f (z)), |s| > 1, has no Valiron deficiency other than exceptional values of R(z). We consider transcendental meromorphic solutions of non-autonomous equation f (sz) =R (z, f (z)), |s| > 1. It is shown that there exists an equation of this form possessing a transcendental meromorphic solution, which has a Valiron deficiency other than a Nevanlinna deficiency. We also give some generalizations of the Eremenko and Sodin theorem for algebraic functions as targets.
{"title":"Deficiency for meromorphic solutions of schröder equations","authors":"K. Ishizaki, Niro Yanagihara ‡","doi":"10.1080/02781070410001731701","DOIUrl":"https://doi.org/10.1080/02781070410001731701","url":null,"abstract":"Eremenko and Sodin proved that meromorphic solution f (z) of the Schröder equation f (sz) = R (f (z)), |s| > 1, has no Valiron deficiency other than exceptional values of R(z). We consider transcendental meromorphic solutions of non-autonomous equation f (sz) =R (z, f (z)), |s| > 1. It is shown that there exists an equation of this form possessing a transcendental meromorphic solution, which has a Valiron deficiency other than a Nevanlinna deficiency. We also give some generalizations of the Eremenko and Sodin theorem for algebraic functions as targets.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117176969","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 : 2004-06-10DOI: 10.1080/02781070412331272523
Sachiko Hamano, Hiroshi Yamaguchi †
We study the variation of the Bergman disk δϵ(t) with center ζ(t) and radius ϵ>0 on the moving Riemann surface R(t) with parameter t in a disk B, and show that, if the total space is a strictly pseudoconvex domain, then, for sufficiently small ϵ > 0, the domain is also pseudoconvex in case ζ(t) is holomorphic on B.
{"title":"A Note on variation of bergman metrics on riemann surfaces under pseudoconvexity","authors":"Sachiko Hamano, Hiroshi Yamaguchi †","doi":"10.1080/02781070412331272523","DOIUrl":"https://doi.org/10.1080/02781070412331272523","url":null,"abstract":"We study the variation of the Bergman disk δϵ(t) with center ζ(t) and radius ϵ>0 on the moving Riemann surface R(t) with parameter t in a disk B, and show that, if the total space is a strictly pseudoconvex domain, then, for sufficiently small ϵ > 0, the domain is also pseudoconvex in case ζ(t) is holomorphic on B.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"93 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116389773","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 : 2004-06-10DOI: 10.1080/02781070410001731657
A. Aleman, Anna-Maria Simbotin
We consider a class of spaces of analytic functions on the unit disc which are Möbius invariant and whose topology is essentially determined by a conformal invariant seminorm. Standard examples of such spaces are the Bloch space, BMOA, the Dirichlet spaces and their recent generalizations QK , which make the object of our interest. We prove a general inequality for the seminorms of dilated functions, radial growth estimates, embedding theorems in Lp -spaces on the unit disc, as well as integral estimates of exponentials of functions in such spaces. Finally, we discuss some properties of the inner-outer factorization for those QK spaces which are contained in the Nevanlinna class.
{"title":"Estimates in Möbius invariant spaces of analytic functions","authors":"A. Aleman, Anna-Maria Simbotin","doi":"10.1080/02781070410001731657","DOIUrl":"https://doi.org/10.1080/02781070410001731657","url":null,"abstract":"We consider a class of spaces of analytic functions on the unit disc which are Möbius invariant and whose topology is essentially determined by a conformal invariant seminorm. Standard examples of such spaces are the Bloch space, BMOA, the Dirichlet spaces and their recent generalizations QK , which make the object of our interest. We prove a general inequality for the seminorms of dilated functions, radial growth estimates, embedding theorems in Lp -spaces on the unit disc, as well as integral estimates of exponentials of functions in such spaces. Finally, we discuss some properties of the inner-outer factorization for those QK spaces which are contained in the Nevanlinna class.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122183474","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: 10.1080/02781070410001710362
I. Lahiri, Abhijit Banerjee †
In this article we prove Tumura–Clunie type theorems which improve some earlier results and as consequences of the main results we extend a theorem of Hayman.
{"title":"Tumura–Clunie Theorem Concerning Differential Polynomials","authors":"I. Lahiri, Abhijit Banerjee †","doi":"10.1080/02781070410001710362","DOIUrl":"https://doi.org/10.1080/02781070410001710362","url":null,"abstract":"In this article we prove Tumura–Clunie type theorems which improve some earlier results and as consequences of the main results we extend a theorem of Hayman.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"66 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":"125461549","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: 10.1080/02781070410001722332
M. Karaev, H. Tuna †
Let denote the vector space of complex-valued functions that are continuous on the closed unit disk and have nth order derivatives in D, which can be extended to functions continuous on . Let denote the subspace of the functions which are analytic in D. We prove that is a Banach algebra with multiplication as Duhamel product and describe its maximal ideal space. We also describe commutant and strong cyclic vectors of the integration operator
{"title":"Description of Maximal Ideal Space of Some Banach Algebra with Multiplication as Duhamel Product","authors":"M. Karaev, H. Tuna †","doi":"10.1080/02781070410001722332","DOIUrl":"https://doi.org/10.1080/02781070410001722332","url":null,"abstract":"Let denote the vector space of complex-valued functions that are continuous on the closed unit disk and have nth order derivatives in D, which can be extended to functions continuous on . Let denote the subspace of the functions which are analytic in D. We prove that is a Banach algebra with multiplication as Duhamel product and describe its maximal ideal space. We also describe commutant and strong cyclic vectors of the integration operator","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"7 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":"121894155","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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