Bulletin of the American Mathematical Society

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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$99.95$

M. Atiyah, R. Bott, and V. K. Patodi, On the heat equation and the index theorem, Invent. Math. 19 (1973), 279–330. MR 650828, DOI 10.1007/BF01425417

Peter B. Gilkey, The index theorem and the heat equation, Mathematics Lecture Series, No. 4, Publish or Perish, Inc., Boston, Mass., 1974. Notes by Jon Sacks. MR 0458504

Peter B. Gilkey, Invariance theory, the heat equation, and the Atiyah-Singer index theorem, 2nd ed., Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1995. MR 1396308

Mark Kac, Can one hear the shape of a drum?, Amer. Math. Monthly 73 (1966), no. 4, 1–23. MR 201237, DOI 10.2307/2313748

D. M. McAvity, Surface energy from heat content asymptotics, J. Phys. A 26 (1993), no. 4, 823–830. MR 1211078

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)