Perturbation Theory for Linear Operators

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.

“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)

• 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.