Book Review
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MathSciNet review:
3688012
Full text of review:
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Book Information:
Author:
Christopher D. Sogge
Title:
Hangzhou lectures on eigenfunctions of the Laplacian
Additional book information:
Annals of Mathematics Studies, Vol. 188,
Princeton University Press,
2014,
xii+193 pp.,
ISBN 978-0-691-16078-8,
US $75.00
Y. Colin de Verdière, Ergodicité et fonctions propres du laplacien, Comm. Math. Phys. 102 (1985), no. 3, 497–502 (French, with English summary). MR 818831
J. J. Duistermaat and V. W. Guillemin, The spectrum of positive elliptic operators and periodic bicharacteristics, Invent. Math. 29 (1975), no. 1, 39–79. MR 405514, DOI 10.1007/BF01405172
Lars Hörmander, The spectral function of an elliptic operator, Acta Math. 121 (1968), 193–218. MR 609014, DOI 10.1007/BF02391913
M. N. Huxley, Exponential sums and lattice points. III, Proc. London Math. Soc. (3) 87 (2003), no. 3, 591–609. MR 2005876, DOI 10.1112/S0024611503014485
A. I. Šnirel′man, Ergodic properties of eigenfunctions, Uspehi Mat. Nauk 29 (1974), no. 6(180), 181–182 (Russian). MR 0402834
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
Christopher D. Sogge, Fourier integrals in classical analysis, Cambridge Tracts in Mathematics, vol. 105, Cambridge University Press, Cambridge, 1993. MR 1205579, DOI 10.1017/CBO9780511530029
Steven Zelditch, Uniform distribution of eigenfunctions on compact hyperbolic surfaces, Duke Math. J. 55 (1987), no. 4, 919–941. MR 916129, DOI 10.1215/S0012-7094-87-05546-3
References
- Y. Colin de Verdière, Ergodicité et fonctions propres du laplacien, Comm. Math. Phys. 102 (1985), no. 3, 497–502 (French, with English summary). MR 818831 (87d:58145)
- J. J. Duistermaat and V. W. Guillemin, The spectrum of positive elliptic operators and periodic bicharacteristics, Invent. Math. 29 (1975), no. 1, 39–79. MR 0405514 (53 \#9307)
- Lars Hörmander, The spectral function of an elliptic operator, Acta Math. 121 (1968), 193–218. MR 0609014 (58 \#29418)
- M. N. Huxley, Exponential sums and lattice points. III, Proc. London Math. Soc. (3) 87 (2003), no. 3, 591–609. MR 2005876 (2004m:11127), DOI 10.1112/S0024611503014485
- A. I. Šnirel′man, Ergodic properties of eigenfunctions, Uspehi Mat. Nauk 29 (1974), no. 6(180), 181–182 (Russian). MR 0402834 (53 \#6648)
- 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 (89d:35131), DOI 10.1016/0022-1236(88)90081-X
- Christopher D. Sogge, Fourier integrals in classical analysis, Cambridge Tracts in Mathematics, vol. 105, Cambridge University Press, Cambridge, 1993. MR 1205579 (94c:35178), DOI 10.1017/CBO9780511530029
- Steven Zelditch, Uniform distribution of eigenfunctions on compact hyperbolic surfaces, Duke Math. J. 55 (1987), no. 4, 919–941. MR 916129 (89d:58129), DOI 10.1215/S0012-7094-87-05546-3
Review Information:
Reviewer:
Andrew Hassell
Affiliation:
Mathematical Sciences Institute,Australian National University, Canberra, Australia
Email:
Andrew.Hassell@anu.edu.au
Journal:
Bull. Amer. Math. Soc.
53 (2016), 693-699
DOI:
https://doi.org/10.1090/bull/1531
Published electronically:
April 4, 2016
Review copyright:
© Copyright 2016
American Mathematical Society
