Differential Operations Of Infinite Order With Real Arguments And Their Applications

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This book is devoted to the theory of infinite-order linear and nonlinear differential operators with several real arguments and their applications to problems of partial differential equations and numerical analysis.Part I develops the theory of pseudodifferential operators with real analytic symbols, the local representatives of which are linear differential operators of infinite order acting in the spaces of basic and generalized functions based on the duality of the spaces of real analytic functions and functionals. Applications to a variety of problems of PDEs and numerical analysis are given. Part II is devoted to the theory of Sobolev-Orlicz spaces of infinite order and the solvability of nonlinear partial differential equations with arbitrary nonlinearities.

Table of contents

CONTENTS
INTRODUCTION
Chapter 1 PRELIMINARIES
Chapter 2 PSEUDO-DIFFERENTIAL OPERATORS WITH REAL ANALYTIC SYMBOLS
Chapter 3 APPLICATIONS TO PSEUDO-DIFFERENTIAL EQUATIONS
Chapter 4 APPROXIMATION METHODS
Chapter 5 A MOLLIFICATION METHOD FOR ILL-POSED PROBLEMS
Chapter 6 NONTRIVIALITY OF SOBOLEV-ORLICZ SPACES OF INFINITE ORDER
Chapter 7 SOME PROPERTIES OF SOBOLEV-ORLICZ SPACES OF INFINITE ORDER
Chapter 8 ELLIPTIC EQUATIONS OF INFINITE ORDER WITH ARBITRARY NONLINEARITIES
Bibliography


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