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Book 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

References [Enhancements On Off] (What's this?)

  • [CdV] 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)
  • [DG] 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)
  • [Hör] Lars Hörmander, The spectral function of an elliptic operator, Acta Math. 121 (1968), 193-218. MR 0609014 (58 #29418)
  • [Hux] M. N. Huxley, Exponential sums and lattice points. III, Proc. London Math. Soc. (3) 87 (2003), no. 3, 591-609. MR 2005876 (2004m:11127), https://doi.org/10.1112/S0024611503014485
  • [Sch] A. I. Šnirelman, Ergodic properties of eigenfunctions, Uspehi Mat. Nauk 29 (1974), no. 6(180), 181-182 (Russian). MR 0402834 (53 #6648)
  • [Sog] 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), https://doi.org/10.1016/0022-1236(88)90081-X
  • [Sog2] Christopher D. Sogge, Fourier integrals in classical analysis, Cambridge Tracts in Mathematics, vol. 105, Cambridge University Press, Cambridge, 1993. MR 1205579 (94c:35178)
  • [Zel] Steven Zelditch, Uniform distribution of eigenfunctions on compact hyperbolic surfaces, Duke Math. J. 55 (1987), no. 4, 919-941. MR 916129 (89d:58129), https://doi.org/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
MSC (2010): Primary 35P20; Secondary 58J40, 58J50
DOI: https://doi.org/10.1090/bull/1531
Published electronically: April 4, 2016
Review copyright: © Copyright 2016 American Mathematical Society
American Mathematical Society