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.

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.