1st Edition
Elementary Introduction to the Theory of Pseudodifferential Operators
By Xavier Saint Raymond
Copyright 1991
116 Pages
by
CRC Press
120 Pages
by
Routledge
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In the 19th century, the Fourier transformation was introduced to study various problems of partial differential equations. Since 1960, this old tool has been developed into a well-organized theory called microlocal analysis that is based on the concept of the pseudo-differential operator. This book provides the fundamental knowledge non-specialists need in order to use microlocal analysis. It is... Read more
Fourier Transformation and Sobolev Spaces: Introduction. Functions in Rn. Fourier Transformation and Distributions in Rn. Sobolev Spaces. Exercises. Notes. Pseudodifferential Symbols: Introduction. Definition and Approximation of Symbols. Oxcillatory Integrals. Operations on Symbols. Exercises. Pseudodifferential Operators: Action in S and S'. Action in Sobolev Spaces. Invariance Under a Change of Variables. Exercises. Notes. Applications: Introduction. Local Solvability of Linear Differential Operators. Wave Front Sets of Solutions of Partial Differential Equations. The Cauchy Problem for the Wave Equation. Exercises. Notes. Index of Notations. References.
Biography
Xavier Saint Raymond
