Böcker av Aref Jeribi

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.