The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis (Classics in Mathematics)

Rating:
Summary: the definitive guide to micro-local analysis
Review: Hormander's four volume guide to linear partial differential operators is the definitive guide to smooth micro-local analysis from the man who invented a large fraction of it.

Micro-local analysis is an approach to the analysis of singularities of variable coefficient linear partial differential equations based on the use of the Fourier transform and of symplectic geometry. Ideas from Hamiltonian physics and quantum theory also feature heavily. The fact that the subject is a mixture of analysis and geometry makes it beautiful and powerful.

The four volume set is hard work and in some ways is more useful as a reference work than as a learning book but on the other hand, all the material is there and the books do reward the reader who is willing to spend the time to study them carefully.

The first volume is the most accessible and the second paperback edition carries the added benefit of included exercises with partial answers which are often highly informative.