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

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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.

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Authors and Affiliations

  1. National School of Electronics and Telecommunications of Sfax, BP 1163 , CP 3018, Sfax, Tunisia

    Salma Charfi

  2. Department of Mathematics, Faculty of Sciences of Sfax, BP 1171 , 3000, Sfax, Tunisia

    Hanen Ellouz

Authors
  1. Salma Charfi
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  2. Hanen Ellouz
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Correspondence to Salma Charfi.

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Charfi, S., Ellouz, H. Riesz Basis of Eigenvectors for Analytic Families of Operators and Application to a Non-symmetrical Gribov Operator. Mediterr. J. Math. 15, 223 (2018). https://doi.org/10.1007/s00009-018-1265-y

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  • DOI: https://doi.org/10.1007/s00009-018-1265-y

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