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

摘要

In a classical paper, Ingham gave a simple proof of an important theorem of Polya on singular points of Dirichlet series under a uniform gap assumption on the exponents. Bernstein generalized Polya'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. (C) 2002 Elsevier Science B.V. All rights reserved. [References: 19]