An introduction to pseudo-differential operators

In this new edition of An Introduction to Pseudo-Differential Operators, the style & scope of the original book are retained. A chapter on the interchange of order of differentiation & integration is added at the beginning to make the book more self-contained, & a chapter on weak solutions of pseudo-differential equations is added at the end to enhance the value of the book as a work on partial differential equations. Several chapters are provided with additional exercises. The bibliography is slightly expanded & an index is added. Contents: Differentiation of Integrals Depending on Parameters; The Convolution; The Fourier Transform; Tempered Distributions; Symbols, Pseudo-Differential Operators & Asymptotic Expansions; A Partition of Unity & 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, 1<p<??;

The Sobolev Spaces Hs,p, ??<s<??, 1??p<??; Closed Linear Operators; Minimal & Maximal Pseudo-Differential Operators; Global Regularity of Elliptic Partial Differential Equations; Weak Solutions of Pseudo-Differential Equations.

1. Differentiation of Integrals Depending on Parameters -- 2. The Convolution -- 3. The Fourier Transform -- 4. Tempered Distributions -- 5. Symbols, Pseudo-Differential Operators and Asymptotic Expansions -- 6. A Partition of Unity and Taylor's Formula -- 7. The Product of Two Pseudo-Differential Operators -- 8. The Formal Adjoint of a Pseudo-Differential Operator -- 9. The Parametrix of an Elliptic Pseudo-Differential Operator -- 10. L[superscript p]-Boundedness of Pseudo-Differential Operators -- 11. The Sobolev Spaces [actual symbol not reproducible] -- 12. Closed Linear Operators -- 13. Minimal and Maximal Pseudo-Differential Operators -- 14. Global Regularity of Elliptic Partial Differential Equations -- 15. Weak Solutions of Pseudo-Differential Equations.