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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

Abstract

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
Journal Name:
Journal of Mathematical Physics
Additional Journal Information:
Journal Volume: 54; Journal Issue: 11; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EIGENVALUES; FUNCTIONS; HILBERT SPACE; MULTIPLICITY; PERTURBATION THEORY

Citation Formats

Ellouz, Hanen, Feki, Ines, and Jeribi, Aref. 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. United States: N. p., 2013. Web. doi:10.1063/1.4826354.
Ellouz, Hanen, Feki, Ines, & Jeribi, Aref. 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. United States. https://doi.org/10.1063/1.4826354
Ellouz, Hanen, Feki, Ines, and Jeribi, Aref. 2013. "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". United States. https://doi.org/10.1063/1.4826354.
@article{osti_22251973,
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},
author = {Ellouz, Hanen and Feki, Ines and Jeribi, Aref},
abstractNote = {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.},
doi = {10.1063/1.4826354},
url = {https://www.osti.gov/biblio/22251973}, journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 11,
volume = 54,
place = {United States},
year = {Fri Nov 15 00:00:00 EST 2013},
month = {Fri Nov 15 00:00:00 EST 2013}
}