An Introduction to Pseudo-Differential Operators

Abstract

Introduction, Notation and Preliminaries Differentiation of Integrals Depending on Parameters The Convolution The Fourier Transform Tempered Distributions Symbols, Pseudo-Differential Operators and Asymptotic Expansions A Partition of Unity and Taylor's Formula The Product of Two Pseudo-Differential Operators The Formal Adjoint of a Pseudo-Differential Operator The Parametrix of an Elliptic Pseudo-Differential Operator Lp-Boundedness of Pseudo-Differential Operators The Sobolev Spaces Hs,p, -∞<s< ∞, 1≤p<∞ Closed Linear Operators Minimal and Maximal Pseudo-Differential Operators Global Regularity of Elliptic Partial Differential Equations Weak Solutions of Pseudo-Differential Equations Garding's Inequality Heat Semigroups Generated by Pseudo-Differential Operators Fredholm Operators Pseudo-Differential Operators with Global Symbols.