Book Review
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MathSciNet review:
1567870
Full text of review:
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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 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 10.1016/0022-1236(84)90076-4
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 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 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 10.1007/BF02399203
J. Nash, Continuity of solutions of parabolic and elliptic equations, Amer. J. Math. 80 (1958), 931–954. MR 100158, DOI 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 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 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 10.1016/0022-1236(88)90081-X
- [D] E. B. Davies, Spectral properties of compact manifolds and changes of metric, Amer. J. Math. (to appear). MR 1037600
- [DGS] E. B. Davies, L. Gross and B. Simon, Hypercontractivity: a bibliographic review, Proceedings of the Hoegh Krohn Memorial Conference.
- [DS] E. B. Davies and B. Simon, Ultra-contractivity and the heat kernel for Schrödin ger operators and Dirichlet Laplacians, J. Funct. Anal. 59 (1984), 335-395. MR 766493
- [FS] E. B. Fabes and D. W. Stroock, A new proof of Moser's parabolic Harnack inequality via the old ideas of Nash, Arch. Rational Mech. Anal. 96 (1986), 327-338. MR 855753
- [F] P. Federbush, A partial alternate derivation of a result of Nelson, J. Math. Phys. 10 (1969), 50-52.
- [G] L. Gross, Logarithmic Sobolev inequalities, Amer. J. Math. 97 (1975), 1061-1083. MR 420249
- [LY] P. Li and S. T. Yau, On the parabolic kernel of the Schrödinger operator, Acta Math. 56 (1986), 153-201. MR 834612
- [Na] J. Nash, Continuity of solutions of parabolic and elliptic equations, Amer. J. Math. 80 (1958), 931-954. MR 100158
- [Ne] E. Nelson, A quartic interaction in two dimensions, Mathematical theory of elementary particles, MIT Press, Cambridge, Mass., 1966, pp. 69-73. MR 210416
- [S 1] C. D. Sogge, Oscillatory integrals and spherical harmonics, Duke Math. J. 53 (1986), 43-65. MR 835795
- [S 2] C. D. Sogge, On the convergence of Riesz means on compact manifolds, Ann. of Math. (2) 126 (1987), 439-447. MR 908154
- [S 3] C. D. Sogge, Concerning the L, J. Funct. Anal. 77 (1988), 123-138. MR 930395
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
