An introduction to pseudo-differential operators

Description

1.Introduction, Notation and Preliminaries -- 2.Differentiation of Integrals Depending on Parameters -- 3.The Convolution -- 4.The Fourier Transform -- 5.Tempered Distributions -- 6.Symbols, Pseudo-Differential Operators and Asymptotic Expansions -- 7.A Partition of Unity and Taylor's Formula -- 8.The Product of Two Pseudo-Differential Operators -- 9.The Formal Adjoint of a Pseudo-Differential Operator -- 10.The Parametrix of an Elliptic Pseudo-Differential Operator -- 11.Lp-Boundedness of Pseudo-Differential Operators -- 12.The Sobolev Spaces Hs,p, --[∞] &lt s &lt [∞], 1 [≤] p &lt [∞] -- 13.Closed Linear Operators -- 14.Minimal and Maximal Pseudo-Differential Operators -- 15.Global Regularity of Elliptic Partial Differential Equations -- 16.Weak Solutions of Pseudo-Differential Equations -- 17.Gårding's Inequality -- 18.Strong Solutions of Pseudo-Differential Equations -- Contents note continued: 19.One-Parameter Semigroups Generated by Pseudo-Differential Operators -- 20.Fredholm Operators -- 21.Fredholm Pseudo-Differential Operators -- 22.Symmetrically Global Pseudo-Differential Operators -- 23.Spectral Invariance of Symmetrically Global Pseudo-Differential Operators.