Book Review

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MathSciNet review: 1567870

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Book Information:

Author: E. B. Davies

Title: Heat kernels and spectral theory

Additional book information: Cambridge University Press, Cambridge, 1989, 197 pp., $49.50. ISBN 0-521-36136-2.

*Spectral properties of compact manifolds and changes of metric*, Amer. J. Math.

**112**(1990), no. 1, 15–39. MR

**1037600**, DOI 10.2307/2374850

*Hypercontractivity: a bibliographic review*, Proceedings of the Hoegh Krohn Memorial Conference.

*Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians*, J. Funct. Anal.

**59**(1984), no. 2, 335–395. MR

**766493**, DOI 10.1016/0022-1236(84)90076-4

*A new proof of Moser’s parabolic Harnack inequality using the old ideas of Nash*, Arch. Rational Mech. Anal.

**96**(1986), no. 4, 327–338. MR

**855753**, DOI 10.1007/BF00251802

*A partial alternate derivation of a result of Nelson*, J. Math. Phys. 10 (1969), 50-52.

*Logarithmic Sobolev inequalities*, Amer. J. Math.

**97**(1975), no. 4, 1061–1083. MR

**420249**, DOI 10.2307/2373688

*On the parabolic kernel of the Schrödinger operator*, Acta Math.

**156**(1986), no. 3-4, 153–201. MR

**834612**, DOI 10.1007/BF02399203

*Continuity of solutions of parabolic and elliptic equations*, Amer. J. Math.

**80**(1958), 931–954. MR

**100158**, DOI 10.2307/2372841

*A quartic interaction in two dimensions*, Mathematical Theory of Elementary Particles (Proc. Conf., Dedham, Mass., 1965) M.I.T. Press, Cambridge, Mass., 1966, pp. 69–73. MR

**0210416**

*Oscillatory integrals and spherical harmonics*, Duke Math. J.

**53**(1986), no. 1, 43–65. MR

**835795**, DOI 10.1215/S0012-7094-86-05303-2

*On the convergence of Riesz means on compact manifolds*, Ann. of Math. (2)

**126**(1987), no. 2, 439–447. MR

**908154**, DOI 10.2307/1971356

*Concerning the $L^p$ norm of spectral clusters for second-order elliptic operators on compact manifolds*, J. Funct. Anal.

**77**(1988), no. 1, 123–138. MR

**930395**, DOI 10.1016/0022-1236(88)90081-X

Review Information:

Reviewer: Robert S. Strichartz

Journal: Bull. Amer. Math. Soc.

**23**(1990), 222-227

DOI: https://doi.org/10.1090/S0273-0979-1990-15936-1