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Complex Analysis and Operator Theory

, Volume 13, Issue 3, pp 839–858 | Cite as

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

  • Salma CharfiEmail author
  • Hanen Ellouz
Article
  • 32 Downloads

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
$$\begin{aligned} T(\varepsilon ):=T_0+\varepsilon T_1 +\varepsilon ^2T_2+\cdots +\varepsilon ^k T_k+\cdots ,~\varepsilon \in \mathbb {C}. \end{aligned}$$
Here \(T_0\) is a closed densely defined linear operator on a separable Hilbert space \(\mathcal{H}\) with domain \(\mathcal{D}(T_0)\) having isolated eigenvalues with multiplicity one and \(T_1, T_2,\ldots \) are linear operators on \(\mathcal{H}\) having the same domain \(\mathcal{D}\supset \mathcal{D}(T_0)\) 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 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.National School of Electronics and Telecommunications of SfaxSfaxTunisia
  2. 2.Department of MathematicsFaculty of Sciences of SfaxSfaxTunisia

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