Spectral Theory and Differential Operators

Cambridge Studies in Advanced Mathematics #42

by E. Brian Davies

This book is an introduction to the theory of partial differential operators. It assumes that the reader has a knowledge of introductory functional analysis, up to the spectral theorem for bounded linear operators on Banach spaces. However, it describes the theory of Fourier transforms and distributions as far as is needed to analyse the spectrum of any constant coefficient partial differential operator. A completely new proof of the spectral theorem for unbounded self-adjoint operators is followed by its application to a variety of second-order elliptic differential operators, from those with discrete spectrum to Schrödinger operators acting on L2(RN). The book contains a detailed account of the application of variational methods to estimate the eigenvalues of operators with measurable coefficients defined by the use of quadratic form techniques. This book could be used either for self-study or as a course text, and aims to lead the reader to the more advanced literature on the subject.

Genres: Mathematics

196 pages, Kindle Edition

First published May 26, 1995

About the author

Edward Brian Davies was a professor of Mathematics, King's College London (1981–2010), and was the author of the popular science book Science in the Looking Glass: What do Scientists Really Know. In 2010, he was awarded a Gauss Lecture by the German Mathematical Society.

Reviews

[HikBook]

Example 1.2.5
The Laplacian -Delta is the most important operator and is also one of the oldest.
It was studied by Laplace in conecction with the theory of gravitation.
The Laplacian operator is symmetric on the space of smooth functions with compact support (or vanishing at the infinity?)