In this new edition of An Introduction to Pseudo-Differential Operators, the style and scope of the original book are retained. A chapter on the interchange of order of differentiation and integration is added at the beginning to make the book more self-contained, and 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 and an index is added.
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; closed linear operators; minimal and maximal pseudo-differential operators; global regularity of elliptic partial differential operators; weak solutions of pseudo-differential equations.