The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis

by Lars Hörmander

The main change in this edition is the inclusion of exercises with answers and hints. This is meant to emphasize that this volume has been written as a general course in modern analysis on a graduate student level and not only as the beginning of a specialized course in partial differen­ tial equations. In particular, it could also serve as an introduction to harmonic analysis. Exercises are given primarily to the sections of gen­ eral interest; there are none to the last two chapters. Most of the exercises are just routine problems meant to give some familiarity with standard use of the tools introduced in the text. Others are extensions of the theory presented there. As a rule rather complete though brief solutions are then given in the answers and hints. To a large extent the exercises have been taken over from courses or examinations given by Anders Melin or myself at the University of Lund. I am grateful to Anders Melin for letting me use the problems originating from him and for numerous valuable comments on this collection. As in the revised printing of Volume II, a number of minor flaws have also been corrected in this edition. Many of these have been called to my attention by the Russian translators of the first edition, and I wish to thank them for our excellent collaboration.

Genres: Mathematics

451 pages, Paperback

First published May 1, 1983

About the author

Lars Valter Hörmander (born 24 January 1931) is a Swedish mathematician who has been called "the foremost contributor to the modern theory of linear partial differential equations". He was awarded the Fields Medal in 1962, the Wolf Prize in 1988, and the Leroy P. Steele Prize in 2006. His Analysis of Linear Partial Differential Operators I–IV is considered a standard work on the subject of linear partial differential operators.

Hörmander completed his Ph.D. in 1955 at Lund University. Hörmander then worked at Stockholm University, at Stanford University, and at the Institute for Advanced Study in Princeton, New Jersey. He returned to Lund University as professor from 1968 until 1996, when he retired with the title of professor emeritus.

http://en.wikipedia.org/wiki/Lars_Hör...

Reviews

[Pollopapas]

En la sección de distribuciones con soporte compacto se menciona que que distribuciones con soporte compacto, pueden ser definidas sobre funciones suaves. (Sección 2.3)

[HikBook]

En la sección de distribuciones con soporte compacto se menciona que que distribuciones con soporte compacto, pueden ser definidas sobre funciones suaves. (Sección 2.3)


En uno de los volúmenes, se menciona la técnica de congelamiento de los coeficientes en un operador de coeficiente variable. Por otro lado, es un ejercicio clásico en un curso básico de física, estudiar: si perforamos el planeta tierra desde un punto A a otro punto B: ¿cómo se comporta un objeto al dejarlo caer por uno de estos puntos? Se suele sugerir al estudiante: Asuma que el planeta no gira.
¿Es posible pensar este supuesto como una técnica de congelamiento?