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Non-orthogonal Fusion Frames of an Analytic Operator and Application to a One-Dimensional Wave Control System

  • Hanen Ellouz
  • Ines FekiEmail author
  • Aref Jeribi
Article
  • 27 Downloads

Abstract

In this paper, we are mainly concerned with a one-dimensional wave control system. We assert the existence of non-orthogonal fusion frames by extending this problem to a theoretical one introduced by Sz. Nagy (Acta Sci Math Szeged 14, 1951). The key idea of this work is based on the estimate inspired from Sz. Nagy (1951) using the spectral analysis method. More precisely, we prove that if the eigenvalues of the unperturbed operator are isolated and with finite multiplicity, we can construct non-orthogonal fusion frames.

Keywords

Non-orthogonal fusion frames Eigenvalues finite multiplicity Eigenprojection wave equation 

Mathematics Subject Classification

47A55 47B38 47H14 47JXX 47J10 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Département de MathématiquesUniversité de Sfax, Ecole supérieure de commerce de SfaxSfaxTunisia

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