What do you think?
Rate this book
The Analysis of Linear Partial Differential Operators II
Brand New. Will be shipped from US.
- GenresMathematics
Hardcover
First published June 1, 1983
8 people want to read
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 of 1 review
Want to read
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.
Displaying 1 of 1 review