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.
- E. B. Davies, Spectral properties of compact manifolds and changes of metric, Amer. J. Math. 112 (1990), no. 1, 15–39. MR 1037600, DOI https://doi.org/10.2307/2374850 [DGS] E. B. Davies, L. Gross and B. Simon, Hypercontractivity: a bibliographic review, Proceedings of the Hoegh Krohn Memorial Conference.
- E. B. Davies and B. Simon, Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians, J. Funct. Anal. 59 (1984), no. 2, 335–395. MR 766493, DOI https://doi.org/10.1016/0022-1236%2884%2990076-4
- E. B. Fabes and D. W. Stroock, 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 https://doi.org/10.1007/BF00251802 [F] P. Federbush, A partial alternate derivation of a result of Nelson, J. Math. Phys. 10 (1969), 50-52.
- Leonard Gross, Logarithmic Sobolev inequalities, Amer. J. Math. 97 (1975), no. 4, 1061–1083. MR 420249, DOI https://doi.org/10.2307/2373688
- Peter Li and Shing-Tung Yau, On the parabolic kernel of the Schrödinger operator, Acta Math. 156 (1986), no. 3-4, 153–201. MR 834612, DOI https://doi.org/10.1007/BF02399203
- J. Nash, Continuity of solutions of parabolic and elliptic equations, Amer. J. Math. 80 (1958), 931–954. MR 100158, DOI https://doi.org/10.2307/2372841
- Edward Nelson, 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
- Christopher D. Sogge, Oscillatory integrals and spherical harmonics, Duke Math. J. 53 (1986), no. 1, 43–65. MR 835795, DOI https://doi.org/10.1215/S0012-7094-86-05303-2
- Christopher D. Sogge, On the convergence of Riesz means on compact manifolds, Ann. of Math. (2) 126 (1987), no. 2, 439–447. MR 908154, DOI https://doi.org/10.2307/1971356
- Christopher D. Sogge, 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 https://doi.org/10.1016/0022-1236%2888%2990081-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
