Böcker av Aref Jeribi

The concept of multivalued linear operators-or linear relations-is the one of the most exciting and influential fields of research in modern mathematics. Applications of this theory can be found in economic theory, noncooperative games, artificial intelligence, medicine, and more. This new book focuses on the theory of linear relations, responding to the lack of resources exclusively dealing with the spectral theory of multivalued linear operators.The subject of this book is the study of linear relations over real or complex Banach spaces. The main purposes are the definitions and characterization of different kinds of spectra and extending the notions of spectra that are considered for the usual one single-valued operator bounded or not bounded. The volume introduces the theory of pseudospectra of multivalued linear operators. The main topics include demicompact linear relations, essential spectra of linear relation, pseudospectra, and essential pseudospectra of linear relations.The volume will be very useful for researchers since it represents not only a collection of a previously heterogeneous material but is also an innovation through several extensions. Beginning graduate students who wish to enter the field of spectral theory of multivalued linear operators will benefit from the material covered, and expert readers will also find sources of inspiration.

This book is devoted to recent developments concerning linear operators, covering topics such as the Cauchy problem, Riesz basis, frames, spectral theory and applications to the Gribov operator in Bargmann space. Also, integral and integro-differential equations as well as applications to problems in mathematical physics and mechanics are discussed. ContentsIntroductionLinear operatorsBasic notations and resultsBasesSemi-groupsDiscrete operator and denseness of the generalized eigenvectorsFrames in Hilbert spacesSummability of seriesI -convergence operatorsI -hypercyclic set of linear operatorsAnalytic operators in Bela Szokefalvi-Nagy's senseBases of the perturbed operator T(I ) Frame of the perturbed operator T(I ) Perturbation method for sound radiation by a vibrating plate in a light fluid Applications to mathematical models Reggeon field theory

This is the first book to tackle the topological fixed point theory for block operator matrices with nonlinear entries in Banach spaces and algebras. The authors present several extensions of Schauder¿s and Krasnosel¿skii¿s fixed point theorems to the class of weakly compact operators acting on Banach spaces and algebras. They also address under which conditions a 2×2 block operator matrix with single- and multi-valued nonlinear entries will have a fixed point. In addition, the book describes applications of fixed point theory to diverse equations.