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Riesz Basis of Eigenvectors for Analytic Families of Operators and Application to a Non-symmetrical Gribov Operator

  • Salma CharfiEmail author
  • Hanen Ellouz
Article
  • 24 Downloads

Abstract

In the present paper, we are mainly concerned with the existence of a Riesz basis related to the Gribov operator
$$\begin{aligned} A^{*2}A^2+\varepsilon (A^* A + A^* (A + A^* )A), \end{aligned}$$
where \(\varepsilon \in \mathbb {C}\); while A is the annihilation operator and \(A^*\) is the creation operator verifying \([A, A^*] = I.\) Through a specific growing inequality, we extend this problem to a theoretical one and we study the invariance of the closure, the comportment of the spectrum as well as the existence of Riesz basis of generalized eigenvectors.

Keywords

Eigenvalues generalized eigenvectors Riesz basis Gribov operator 

Mathematics Subject Classification

47B25 34L10 

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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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