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Title: On a Riesz basis of exponentials related to the eigenvalues of an analytic operator and application to a non-selfadjoint problem deduced from a perturbation method for sound radiation

In the present paper, we prove that the family of exponentials associated to the eigenvalues of the perturbed operator T(ε) ≔ T{sub 0} + εT{sub 1} + ε{sup 2}T{sub 2} + … + ε{sup k}T{sub k} + … forms a Riesz basis in L{sup 2}(0, T), T > 0, where ε∈C, T{sub 0} is a closed densely defined linear operator on a separable Hilbert space H with domain D(T{sub 0}) having isolated eigenvalues with multiplicity one, while T{sub 1}, T{sub 2}, … are linear operators on H having the same domain D⊃D(T{sub 0}) and satisfying a specific growing inequality. After that, we generalize this result using a H-Lipschitz function. As application, we consider a non-selfadjoint problem deduced from a perturbation method for sound radiation.
Authors:
; ;  [1]
  1. Département de Mathématiques, Université de Sfax, Faculté des sciences de Sfax, Route de soukra Km 3.5, B.P. 1171, 3000 Sfax (Tunisia)
Publication Date:
OSTI Identifier:
22251973
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 11; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EIGENVALUES; FUNCTIONS; HILBERT SPACE; MULTIPLICITY; PERTURBATION THEORY