Frame of Exponentials Related to Analytic Families Operators and Application to a Non-self Adjoint Problem of Radiation of a Vibrating Structure in a Light Fluid

Frame of Exponentials Related to Analytic Families Operators and Application to a Non-self... Complex Anal. Oper. Theory Complex Analysis https://doi.org/10.1007/s11785-018-0807-4 and Operator Theory Frame of Exponentials Related to Analytic Families Operators and Application to a Non-self Adjoint Problem of Radiation of a Vibrating Structure in a Light Fluid 1 2 Salma Charfi · Hanen Ellouz Received: 9 January 2018 / Accepted: 26 May 2018 © Springer International Publishing AG, part of Springer Nature 2018 Abstract In the present paper, we investigate under sufficient conditions the existence of frames of exponential families, where the exponents coincide with the eigenvalues of the perturbed operator 2 k T (ε) := T + εT + ε T + ··· + ε T + ··· ,ε ∈ C. 0 1 2 k Here T is a closed densely defined linear operator on a separable Hilbert space H with domain D(T ) having isolated eigenvalues with multiplicity one and T , T ,... are 0 1 2 linear operators on H having the same domain D ⊃ D(T ) and satisfying a specific growing inequality. The obtained results are applied to a non-self adjoint problem deduced from a perturbation method for sound radiation. Keywords Frames of exponentials · Eigenvalues · Elastic membrane · Integro- differential operator Communicated by http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Complex Analysis and Operator Theory Springer Journals

Frame of Exponentials Related to Analytic Families Operators and Application to a Non-self Adjoint Problem of Radiation of a Vibrating Structure in a Light Fluid

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Mathematics, general; Operator Theory; Analysis
ISSN
1661-8254
eISSN
1661-8262
D.O.I.
10.1007/s11785-018-0807-4
Publisher site
See Article on Publisher Site

Abstract

Complex Anal. Oper. Theory Complex Analysis https://doi.org/10.1007/s11785-018-0807-4 and Operator Theory Frame of Exponentials Related to Analytic Families Operators and Application to a Non-self Adjoint Problem of Radiation of a Vibrating Structure in a Light Fluid 1 2 Salma Charfi · Hanen Ellouz Received: 9 January 2018 / Accepted: 26 May 2018 © Springer International Publishing AG, part of Springer Nature 2018 Abstract In the present paper, we investigate under sufficient conditions the existence of frames of exponential families, where the exponents coincide with the eigenvalues of the perturbed operator 2 k T (ε) := T + εT + ε T + ··· + ε T + ··· ,ε ∈ C. 0 1 2 k Here T is a closed densely defined linear operator on a separable Hilbert space H with domain D(T ) having isolated eigenvalues with multiplicity one and T , T ,... are 0 1 2 linear operators on H having the same domain D ⊃ D(T ) and satisfying a specific growing inequality. The obtained results are applied to a non-self adjoint problem deduced from a perturbation method for sound radiation. Keywords Frames of exponentials · Eigenvalues · Elastic membrane · Integro- differential operator Communicated by

Journal

Complex Analysis and Operator TheorySpringer Journals

Published: Jun 5, 2018

References

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