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The Analysis of Linear Partial Differential Operators II: Differential Operators with Constant Coefficients
From the reviews: "With the basic theory of distributions and Fourier analysis set down, volume II proceeds deeper into the study of linear PDE, particularly with constant coefficients. Detailed analysis is made of the regularity of certain fundamental solutions of general constant coefficient operators P(D), including a classification of when P(D) is hypoelliptic." American Mathematical Monthly#1 "The books are very careful written. They give a good introduction into the areas considered. The reviewer's opinion is that L. Hörmander`s books will be a basis for studying differential equations for a long time." ZAMM#2
- GenresMathematics
392 pages, Hardcover
First published June 1, 1983
8 people want to read
About the author
Lars Hörmander
29 books2 followersLars 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...
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...
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January 8, 2024Chapter X. Existence and Approximation of solutions of differential equations.
Definition 10.1.1. A positive function k in R is a temperate weight function if k(xi+eta)<= (1+C|xi|)^N k(eta))
This set is denoted as K.
Definition 10.1.6. If k in K, B_{p,k} is the set of all tempered distributions u such that Fourier(u) is a function and
|u|_{p,k}:=[int |k(xi) Fourier(u)(xi)|^pdxi]^(1/p) < infinity.
If p=infinity,
|u|_{infinity, k}= essential supremum of k(xi)fourier(u)(xi) (standard)
Theorem 10.1.7. Schwartz space subset B_{p,k} subset tempered distributions (in topological sense)
Chapter XIII. Differential operators of constant strength.
Differential operators defined on the space B_{k,p} are studied.
Definition 10.1.1. A positive function k in R is a temperate weight function if k(xi+eta)<= (1+C|xi|)^N k(eta))
This set is denoted as K.
Definition 10.1.6. If k in K, B_{p,k} is the set of all tempered distributions u such that Fourier(u) is a function and
|u|_{p,k}:=[int |k(xi) Fourier(u)(xi)|^pdxi]^(1/p) < infinity.
If p=infinity,
|u|_{infinity, k}= essential supremum of k(xi)fourier(u)(xi) (standard)
Theorem 10.1.7. Schwartz space subset B_{p,k} subset tempered distributions (in topological sense)
Chapter XIII. Differential operators of constant strength.
Differential operators defined on the space B_{k,p} are studied.
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