Spectral Theory and Differential Operators

Erscheinungsjahr 2003
ISBN: 978-0-521-58710-5
Verlag: Cambridge University Press

Buch, Englisch, Band 42, 192 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 293 g

Reihe: Cambridge Studies in Advanced Mathematics

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.

Autoren/Hrsg.

Davies, E. Brian

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

1. The fundamental ideas; 2. The spectral theorem; 3. Translation invariant operators; 4. The variation methods; 5. Further spectral results; 6. Dirichlet boundary conditions; 7. Neumann boundary conditions; 8. Schrödinger operators.