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Perturbation Theory for Linear Operators

Denseness and Bases with Applications

  • Book
  • © 2021

Overview

Authors:
  1. Aref Jeribi

    1. Department of Mathematics, University of Sfax, Sfax, Tunisia

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  • Discusses key topics on spectral theory along with recent developments in the area

  • Includes applications in mathematical physics and mechanics

  • Presents results motivated by physical problems

  • Appeals to students, researchers, pure analysts and mathematicians

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xxvi
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  2. Basic Notations and Results

    • Aref Jeribi
    Pages 1-40

  3. Analysis with Operators

    • Aref Jeribi
    Pages 41-82

  4. Series of Complex Terms

    • Aref Jeribi
    Pages 83-101

  5. Carleman-Class

    • Aref Jeribi
    Pages 103-129

  6. The Evolutionary Problem

    • Aref Jeribi
    Pages 131-175

  7. Completeness Criteria of the Space of Generalized Eigenvectors of Non-Self-Adjoint Operators

    • Aref Jeribi
    Pages 177-205

  8. Bases on Hilbert and Banach Spaces

    • Aref Jeribi
    Pages 207-254

  9. On a Riesz Basis of Finite-Dimensional Invariant Subspaces

    • Aref Jeribi
    Pages 255-302

  10. Analytic Operators in Feki-Jeribi-Sfaxi’s Sense

    • Aref Jeribi
    Pages 303-333

  11. On a Schauder and Riesz Bases of Eigenvectors of an Analytic Operator

    • Aref Jeribi
    Pages 335-359

  12. On the Asymptotic Behavior of the Eigenvalues of an Analytic Operator in the Sense of Kato

    • Aref Jeribi
    Pages 361-388

  13. On the Basis Property of Root Vectors Related to a Non-self-adjoint Analytic Operator

    • Aref Jeribi
    Pages 389-407

  14. Perturbation Method for Sound Radiation by a Vibrating Plate in a Light Fluid

    • Aref Jeribi
    Pages 409-436

  15. Gribov Operator in Bargmann Space

    • Aref Jeribi
    Pages 437-463

  16. Applications in Mathematical Physics and Mechanics

    • Aref Jeribi
    Pages 465-503

  17. Back Matter

    Pages 505-509
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Keywords

About this book

This book discusses the important aspects of spectral theory, in particular, the completeness of generalised eigenvectors, Riesz bases, semigroup theory, families of analytic operators, and Gribov operator acting in the Bargmann space. Recent mathematical developments of perturbed non-self-adjoint operators are discussed with the completeness of the space of generalized eigenvectors, bases on Hilbert and Banach spaces and asymptotic behavior of the eigenvalues of these operators. Most results in the book are motivated by physical problems, such as the perturbation method for sound radiation by a vibrating plate in a light fluid, Gribov operator in Bargmann space and other applications in mathematical physics and mechanics. This book is intended for students, researchers in the field of spectral theory of linear non self-adjoint operators, pure analysts and mathematicians.

Reviews

“The exposition of this book is clear, structured and almost self-contained. Several results related to Fredholm and spectral theories for Hilbert space operators are discussed in detail. A rich bibliography is provided at the end of each chapter. The book is addressed to students, researchers in the field of spectral theory of linear non-self-adjoint operators, and mathematicians interested in applications in mathematical physics. I think that pure analysts will have some new problems to tackle.” (Bilel Krichen, Mathematical Reviews, September, 2022)

“This book provides a very good collection of results for the study of the structural property of unbounded linear operators with compact resolvent, in particular, for the study of non-selfadjoint operators in Hilbert spaces.” (Gen Qi Xu, zbMATH 1483.47001, 2022)

Authors and Affiliations

  • Department of Mathematics, University of Sfax, Sfax, Tunisia

    Aref Jeribi

About the author

AREF JERIBI is Professor at the Department of Mathematics, University of Sfax, Tunisia. He completed his Habilitation of Mathematics and Applications in 2002 at the University of Sfax, Tunisia, and defended his PhD thesis in 1998 at the University of Corsica Pasquale Paoli, France. His research interests include spectral theory, matrix operators, transport theory, Gribov operator, Bargmann space, fixed point theory, Riesz basis, and linear relations. He is an author of 5 books, including Spectral Theory and Applications of Linear Operators and Block Operator Matrices (Springer Nature, 2015) and 117 research articles published in reputed journals and conference proceedings.

Bibliographic Information

  • Book Title: Perturbation Theory for Linear Operators

  • Book Subtitle: Denseness and Bases with Applications

  • Authors: Aref Jeribi

  • DOI: https://doi.org/10.1007/978-981-16-2528-2

  • Publisher: Springer Singapore

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021

  • Hardcover ISBN: 978-981-16-2527-5Published: 29 July 2021

  • Softcover ISBN: 978-981-16-2530-5Published: 30 July 2022

  • eBook ISBN: 978-981-16-2528-2Published: 28 July 2021

  • Edition Number: 1

  • Number of Pages: XXVI, 509

  • Number of Illustrations: 16 b/w illustrations

  • Topics: Operator Theory

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