Spectral Theory and Applications of Linear Operators and Block Operator Matrices

ISBN-13: 9783319175652 / Angielski / Twarda / 2015 / 599 str.

Aref Jeribi

Opis

Examining recent mathematical developments in the study of Fredholm operators, spectral theory and block operator matrices, with a rigorous treatment of classical Riesz theory of polynomially-compact operators, this volume covers both abstract and applied developments in the study of spectral theory. These topics are intimately related to the stability of underlying physical systems and play a crucial role in many branches of mathematics as well as numerous interdisciplinary applications. By studying classical Riesz theory of polynomially compact operators in order to establish the existence results of the second kind operator equations, this volume will assist the reader working to describe the spectrum, multiplicities and localization of the eigenvalues of polynomially-compact operators.

Recenzje

"The author studies specifically some relevant aspects of the spectral theory for block operator matrices from a new standpoint and incorporates recent results of his own works. ... the book provides a large variety of important applications in many branches of mathematics as well as physics, biology, and some open questions are given, too. This book may be of interest for both experienced researchers and graduate students." (Carlos R. Carpintero, zbMATH 1354.47001, 2017)

Spis treści

 Introduction.- Fredholm Operators and Riesz Theory.- Abstract Cauchy Problem.- Fredholm Theory Related to Some Measures.-  Pertubation Results.- Essential Spectra of Linear Operators.-  Essentia Pseudo-spectra.- S-Essential Spectra.- Essential Spectra of 2 X 2 Block Operator Matrices.- Essential Spectra of 3 X 3 Block Operator Matrices.- Applications in Mathematical Physics and Biology. 

O autorze

Prof. Dr. Aref Jeribi is a Professor in the Department of Mathematics at the University of Sfax in Sfax, Tunisia.