View More View Less
  • 1 Università di Roma “La Sapienza” Dipartimento di Matematica P.le Aldo Moro 2 00185 Roma Italy P.le Aldo Moro 2 00185 Roma Italy
  • 2 Université Louis Pasteur et CNRS Institut de Recherche Mathématique Avancée 7, rue René Descartes 67084 Strasbourg Cédex France 7, rue René Descartes 67084 Strasbourg Cédex France
  • 3 Università di Roma “La Sapienza” Via A. Scarpa, 16 00161 Roma Italy Via A. Scarpa, 16 00161 Roma Italy
Restricted access

Abstract  

Completing a series of works begun by Wiener [34], Paley and Wiener [28] and Ingham [9], a far-reaching generalization of Parseval"s identity was obtained by Beurling [4] for nonharmonic Fourier series whose exponents satisfy a uniform gap condition. Later this gap condition was weakened by Ullrich [33], Castro and Zuazua [5], Jaffard, Tucsnak and Zuazua [11] and then in [2] in some particular cases. In this paper we prove a general theorem which contains all previous results. Furthermore, applying a different method, we prove a variant of this theorem for nonharmonic Fourier series with vector coefficients. This result, partly motivated by control-theoretical applications, extends several earlier results obtained in [15] and [2]. Finally, applying these results we obtain an optimal simultaneous observability theorem concerning a system of vibrating strings.

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Nov 2020 0 0 0
Dec 2020 0 0 0
Jan 2021 1 0 0
Feb 2021 0 0 0
Mar 2021 2 0 0
Apr 2021 0 0 0
May 2021 0 0 0