Perturbation Theory for Linear Operators

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.

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

Autorentext

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.

Inhalt

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.