Spectral Functions in Mathematics and Physics

by Klaus Kirsten

Overview

The literature on the spectral analysis of second order elliptic differential operators contains a great deal of information on the spectral functions for explicitly known spectra. The same is not true, however, for situations where the spectra are not explicitly known. Over the last several years, the author and his colleagues have developed new,

Product Details

ISBN-13:	9781000738155
Publisher:	CRC Press
Publication date:	12/13/2001
Sold by:	Barnes & Noble
Format:	eBook
Pages:	400
File size:	5 MB

About the Author

Klaus Kirsten is a post-doctoral associate at the Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany.

Table of Contents

Introduction. A First Look at Zeta Functions and Heat Traces. Zeta Functions on Generalized Cones and Related Manifolds. Calculation of Heat Kernel Coeffcients via Special Cases. Heat Content Asymptotics. Functional Determinants. Casimir Energies. Ground State Energies under the Influence of External Fields. Bose-Einstein Condensation of Ideal Bose Gases under External Conditions. Conclusions. Appendices. References. Index.

Editorial Reviews

Presents new methods for the exact analysis of spectral functions under external conditions, focusing on zeta functions of second-order elliptic differential operators. The first technique analyzes spectral functions for Laplace-type operators for cases where the spectrum is not known explicitly, but only implicitly. The author applies the methods to derive heat kernel coefficients for smooth Riemannian manifolds with various boundary conditions, functional determinants, Casimir energies with spherically symmetric boundaries, and the Bose-Einstein condensation. Annotation c. Book News, Inc., Portland, OR (booknews.com)