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The Analysis of Linear Partial Differential Operators II: Differential Operators with Constant Coefficients

Lars Hörmander
Springer Verlag
Publication Date: 
Number of Pages: 
Classics in Mathematics
[Reviewed by
Fernando Q. Gouvêa
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This is a reprint, in Springer's Classics in Mathematics series, of a book first published in 1983 in the much pricier Grundlehren series. It is the second volume in a four-volume set which was described in the original "Telegraphic Review" as "a monumental work by a master". Full reviews of the first two volumes appeared in The American Mathematical Monthly (December 1985), SIAM Review (June 1985), and the Bulletin of the American Mathematical Society (1984). They are all worth reading.

This volume focuses on linear partial differential operators with constant coefficients, but not exclusively so. The book is more a compendium than a textbook; there are no exercises. Each chapter ends with notes on the literature, and there is a large bibliography.

The binding of this softcover reprint seems quite good, but the quality of the printing is not so impressive (perhaps because it is a photographic reproduction of material printed in an early laser printer?).

Overall, it is great to have this book back at an affordable price. It really does deserve to be described as a classic.

 Fernando Q. Gouvêa is the editor of MAA Reviews.

Introduction.- Existence and Approximation of Solutions of Differential Equations.- Interior Regularity of Solutions of Differential Equations.- The Cauchy and Mixed Problems.- Differential Operators of Constant Strength.- Scattering Theory.- Analytic Function Theory and Differential Equations.- Convolution Equations.- Appendix A: Some Algebraic Lemmas.- Bibliography.- Index.- Index of Notation.