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On the quasi-Fredholm and Saphar spectrum of strongly continuous Cosine operator function

Hamid Boua

Hamid Boua

Department of Mathematics and Computer Science, Pluridisciplinary Faculty of Nador, Mohammed First University
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Boua, Hamid
  
Nov 22, 2020
On the quasi-Fredholm and Saphar spectrum of strongly continuous Cosine operator function's Cover Image
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Published Online: Nov 22, 2020
Page range: 80 - 87
Received: Aug 08, 2020
Accepted: Nov 08, 2020
DOI: https://doi.org/10.2478/mjpaa-2021-0008
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© 2020 Hamid Boua, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Let (C(t))t∈𝕉 be a strongly continuous cosine family and A be its infinitesimal generator. In this work, we prove that, if C(t) – coshλt is Saphar (resp. quasi-Fredholm) operator and λt /∉iπ𝕑, then A – λ2 is also Saphar (resp. quasi-Fredholm) operator. We show by counter-example that the converse is false in general.

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English
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3 times per year
Journal Subjects:
Mathematics, Analysis, Differential Equations and Dynamical Systems, Probability and Statistics, Numerical and Computational Mathematics
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