Elementary Introduction to the Theory of Pseudodifferential Operators

ISBN-13: 9780849371585 / Angielski / Twarda / 1991 / 120 str.

Xavier Saint Raymond; Raymond Saint Raymond; Xavier Saint Raymond

Opis

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 explains the origin of the theory.

Spis treści

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.

O autorze

Xavier Saint Raymond