Book Review

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Book Information:

Author: Klaus Kirsten

Title: Spectral functions in mathematics and physics

Additional book information: Chapman & Hall/CRC, Boca Raton, FL, 2002, xiv+382 pp., ISBN 1-58488-259-X, US$99.95

Author: Peter B. Gilkey

Title: Asymptotic formulae in spectral geometry

Additional book information: Studies in Advanced Mathematics, vol. 43, Chapman & Hall/CRC, Boca Raton, FL, 2004, viii+ 304 pp., ISBN 1-58488-358-8, US$99.95

**1.**M. F. Atiyah, R. Bott, and V. K. Patodi,*On the heat equation and the index theorem*, Invent. Math.**19**(1973), 279-330. MR**0650828 (58:31287)****2.**P. B. Gilkey,*The Index Theorem and the Heat Equation*(Math. Lecture Series**4**), Publish or Perish, Boston, MA, 1974. MR**0458504 (56:16704)****3.**P. B. Gilkey,*Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem*(Math. Lecture Series**11**), Publish or Perish, Wilmington, DE, 1984; 2nd edition (Studies Adv. Math.**16**), CRC Press, Boca Raton, FL, 1995. MR**1396308 (98b:58156)****4.**M. Kac,*Can one hear the shape of a drum?*, Amer. Math. Monthly**73**(1966), Part II, 1-23. MR**0201237 (34:1121)****5.**D. M. McAvity,*Surface energy from heat content asymptotics*, J. Phys. A**26**(1993), 823-830. MR**1211078 (94c:58200)**

Review Information:

Reviewer: S. A. Fulling

Affiliation: Texas A&M University

Email: fulling@math.tamu.edu

Journal: Bull. Amer. Math. Soc.

**43**(2006), 423-427

MSC (2000): Primary 58J35

Published electronically: April 18, 2006

Review copyright: © Copyright 2006 American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.