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

by Lars Hörmander

Vol. 1 of Lars Hörmander's influential 4-volume treatise is a detailed exposition of the theory of distributions. From the "In order to illustrate the richness of the in my review of the 1983 edition [...] I gave a list of 20 subjects which were new compared to Hörmander's book of 1963. Most of these subjects concern important, basic and highly nontrivial theorems in analysis. Hörmander's treatment of these is extremely clear and efficient and often highly original. [...] Most of the exercises are witty, with an interesting point. The phrasing of both the exercises and the answers and hints is very careful [...] In all, the book can be highly recommended, both as a textbook for advanced students, and as background and reference for introductory courses on distributions and Fourier analysis." J.J. Duistermaat in Mededelingen van het Wiskundig Genootschap

Genres: Mathematics

440 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?