Dirichlet series and simultaneous observability: two problems solved by the same approach

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• 作者：Komornik ; Vilmos ; Loreti ; Paola
• 关键词：Dirichlet series ; Singularity ; Fourier series ; Observability ; Wave equation
• 刊名：Systems and Control Letters
• 出版年：2003
• 出版时间：March 15, 2003
• 年：2003
• 卷：48
• 期：3-4
• 页码：221-227
• 全文大小：149 K

文摘

In a classical paper, Ingham gave a simple proof of an important theorem of Pólya on singular points of Dirichlet series under a uniform gap assumption on the exponents. Bernstein generalized Pólya's theorem by weakening this gap condition. We give a simpler proof of Bernstein's theorem by applying a recent generalization of Ingham's theorem. Furthermore, we also solve a simultaneous observability problem by using this theory.