Generalized weighted Bergman–Dirichlet and Bargmann–Dirichlet spaces: explicit formulae for reproducing kernels and asymptotics

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• 作者：A. El Hamyani ; A. Ghanmi ; A. Intissar…
• 关键词：Weighted Bergman–Dirichlet spaces ; Weighted Bargmann–Dirichlet spaces ; Reproducing kernel function ; Hypergeometric functions ; Asymptotic behavior
• 刊名：Annals of Global Analysis and Geometry
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：49
• 期：1
• 页码：59-72
• 全文大小：477 KB
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  14.Zhu, K.: Analysis on Fock spaces. In: Graduate Texts in Mathematics, vol. 263. Springer, New York (2012)
  
• 作者单位：A. El Hamyani (1)
  A. Ghanmi (1)
  A. Intissar (1)
  Z. Mouhcine (1)
  M. Souid El Aïnin (1)
  
  1. E.D.P. and Spectral Geometry, Laboratory of Analysis and Applications-URAC/03, Department of Mathematics, Faculty of Sciences, Mohammed V University, P.O. Box 1014, Rabat, Morocco
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Mathematical and Computational Physics
  Group Theory and Generalizations
  Geometry
  
• 出版者：Springer Netherlands
• ISSN：1572-9060

文摘

We introduce new functional spaces generalizing the weighted Bergman and Dirichlet spaces on the complex disk \(\mathbb {D}_R=D(0,R)\) as well as the Bargmann–Fock spaces on the whole complex plane \(\mathbb C\). We give a complete description of the considered spaces. Mainly, we are interested in giving explicit formulas for their reproducing kernel functions and their asymptotic behavior as R goes to infinity. Keywords Weighted Bergman–Dirichlet spaces Weighted Bargmann–Dirichlet spaces Reproducing kernel function Hypergeometric functions Asymptotic behavior