An Ingham--Müntz type theorem and simultaneous observation problems
Vilmos Komornik - Département de mathématique, Université de Strasbourg, 7, rue René Descartes, 67084 Strasbourg Cedex, France (email)
Abstract: We establish a theorem combining the estimates of Ingham and Müntz--Szász. Moreover, we allow complex exponents instead of purely imaginary exponents for the Ingham type part or purely real exponents for the Müntz--Szász part. A very special case of this theorem allows us to prove the simultaneous observability of some string--heat and beam--heat systems.
Keywords: Observability, non-harmonic Fourier series, Ingham's theorem, Müntz--Szász theorem, wave equation, heat equation, beam equation.
Received: April 2015; Revised: July 2015; Available Online: September 2015.
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