An Ingham--Müntz type theorem and simultaneous observation problems

Vilmos  Komornik; Gérald  Tenenbaum

doi:10.3934/eect.2015.4.297

Article Contents

2015, Volume 4, Issue 3: 297-314. Doi: 10.3934/eect.2015.4.297

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An Ingham--Müntz type theorem and simultaneous observation problems

Vilmos Komornik^1, and
Gérald Tenenbaum^2,

1.
Département de mathématique, Université de Strasbourg, 7, rue René Descartes, 67084 Strasbourg Cedex
2.
Institut Élie Cartan, Université de Lorraine, BP 70239, 54506 Vandœuvre-lès-Nancy Cedex

Received: March 31, 2015

Revised: June 30, 2015

Published: August 2015

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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.

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Mathematics Subject Classification: Primary: 42C99; Secondary: 93B07.

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