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Perturbation Theory for Linear Operators Denseness and Bases with Applications

Jeribi Aref
Innbundet / 2021 / Engelsk

Produktdetaljer

ISBN
9789811625275
Publisert
2021-07-29
Utgiver
Vendor
Springer Verlag, Singapore
Høyde
235 mm
Bredde
155 mm
Aldersnivå
Research, P, 06
Språk
Product language
Engelsk
Format
Product format
Innbundet

Forfatter
Jeribi Aref

Biographical note

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.

Perturbation Theory for Linear Operators Denseness and Bases with Applications

Jeribi Aref
Innbundet / 2021 / Engelsk
Jeribi Aref
Innbundet / 2021 / Engelsk
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“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)<br />“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)

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.
Les mer
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.
Les mer
1. Basic notations and results2 Analysis with operators3 Series of complex terms.- 4. Carleman-class.- 5. The evolutionary problem6 Completeness criteria of the space of generalized eigenvectors of non-self-adjoint operators.- 7. Bases on Hilbert and Banach spaces.- 8. On a Riesz basis of finite-dimensional invariant subspaces.- 9. Analytic operators in Feki-Jeribi-Sfaxi's sense.- 10. On a Schauder and Riesz bases of eigenvectors of an analytic operator.- 11. On the asymptotic behavior of the eigenvalues of an analytic operator in the sense of Kato.- 12. On the basis property of root vectors related to a non-self-adjoint analytic operator.- 13. Perturbation method for sound radiation by a vibrating plate in a light fluid.- 14. Gribov operator in Bargmann space15 Applications in Mathematical Physics and Mechanics.
Les mer
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.
Les mer
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
Les mer
GPSR Compliance The European Union's (EU) General Product Safety Regulation (GPSR) is a set of rules that requires consumer products to be safe and our obligations to ensure this. If you have any concerns about our products you can contact us on ProductSafety@springernature.com. In case Publisher is established outside the EU, the EU authorized representative is: Springer Nature Customer Service Center GmbH Europaplatz 3 69115 Heidelberg, Germany ProductSafety@springernature.com
Les mer

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“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)<br />“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)

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.
Les mer
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.
Les mer
1. Basic notations and results2 Analysis with operators3 Series of complex terms.- 4. Carleman-class.- 5. The evolutionary problem6 Completeness criteria of the space of generalized eigenvectors of non-self-adjoint operators.- 7. Bases on Hilbert and Banach spaces.- 8. On a Riesz basis of finite-dimensional invariant subspaces.- 9. Analytic operators in Feki-Jeribi-Sfaxi's sense.- 10. On a Schauder and Riesz bases of eigenvectors of an analytic operator.- 11. On the asymptotic behavior of the eigenvalues of an analytic operator in the sense of Kato.- 12. On the basis property of root vectors related to a non-self-adjoint analytic operator.- 13. Perturbation method for sound radiation by a vibrating plate in a light fluid.- 14. Gribov operator in Bargmann space15 Applications in Mathematical Physics and Mechanics.
Les mer
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.
Les mer
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
Les mer
GPSR Compliance The European Union's (EU) General Product Safety Regulation (GPSR) is a set of rules that requires consumer products to be safe and our obligations to ensure this. If you have any concerns about our products you can contact us on ProductSafety@springernature.com. In case Publisher is established outside the EU, the EU authorized representative is: Springer Nature Customer Service Center GmbH Europaplatz 3 69115 Heidelberg, Germany ProductSafety@springernature.com
Les mer

Produktdetaljer

ISBN
9789811625275
Publisert
2021-07-29
Utgiver
Vendor
Springer Verlag, Singapore
Høyde
235 mm
Bredde
155 mm
Aldersnivå
Research, P, 06
Språk
Product language
Engelsk
Format
Product format
Innbundet

Forfatter
Jeribi Aref

Biographical note

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.

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