الصفحة 1
الصفحة 1
Methods in Nonlinear Analysis
Nonlinear analysis has developed rapidly in the last three decades. Theories, techniques and results in many different branches of mathematics have been combined in solving nonlinear problems. This book collects and reorganizes up-to-date materials scattered throughout the literature from the methodology point of view, and presents them in a systematic way. It contains the basic theories and methods with many interesting problems in partial and ordinary differential equations, differential geometry and mathematical physics as applications.There are five chapters that cover linearization, fixed-point theorems based on compactness and convexity, topological degree theory, minimization and topological variational methods. Each chapter combines abstract, classical and applied analysis. Particular topics included are bifurcation, perturbation, gluing technique, transversality, Nash–Moser technique, Ky Fan's inequality and Nash equilibrium in game theory, setvalued mappings and differential equations with discontinuous nonlinear terms, multiple solutions in partial differential equations, direct method, quasiconvexity and relaxation, Young measure, compensation compactness method and Hardy space, concentration compactness and best constants, Ekeland variational principle, infinite-dimensional Morse theory, minimax method, index theory with group action, and Conley index theory.
Functions of a-Bounded Type in the Half-Plane
This is a unique book related to the theory of functions of a-bounded type in the half-plane of the complex plane, which is constructed by application of the Liouville integro-differential operator. In addition, the book contains improvements of several results such as the Phragmen-Lindelof Principle and Nevanlinna Factorization in the Half-Plane, and offers a new, equivalent definition of the classical Hardy spaces in the half-plane. The last chapter of the book presents an application of the constructed theory as well as M.M.Djrbashian’s theory of Nevanlinna type classes in the disc in the spectral theory of linear operators. This is a solution of a problem repeatedly stated by M.G.Krein and being of special interest for a long time.
An Introduction to Operators on the Hardy-Hilbert Space
The subject of this book is operator theory on the Hardy space H2, also called the Hardy-Hilbert space. The goal is to provide an elementary and engaging introduction to this subject that will be readable by everyone who has understood introductory courses in complex analysis and in functional analysis.
