Application of Functional Calculus to Complex Cauchy Problems

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• 作者：Stéphane Rigat (1)
  
• 关键词：Cauchy problem ; functional calculus ; analytic functionals ; Fantappiè transform ; 32A15 ; 32A25 ; 32A27 ; 35C05 ; 35E15 ; 35E20 ; 44A45
• 刊名：Computational Methods and Function Theory
• 出版年：2007
• 出版时间：December 2007
• 年：2007
• 卷：7
• 期：2
• 页码：509-526
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• 作者单位：Stéphane Rigat (1)
  
  1. Centre de Mathématiques et Informatique, LATP UMR 6632, 39, rue F. Joliot-Curie, 13453, Marseille Cedex 13, France
  
• ISSN：2195-3724

文摘

In this paper, we study an approach of functional calculus in several variables developed for a particular case of commuting operators. This approach, which differs from the classical one, originates in the works of Fan-tappiè. It is useful to obtain explicit solution to partial differential equations and holomorphic Cauchy problems, as well as to make a link between the holomorphic functional calculus, the theory of analytic functionals, and the Fantappiè transform of analytic functionals.