Bulletin of the American Mathematical Society

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Book Information:

Author: David Gurarie
Title: Symmetries and Laplacians: Introduction to harmonic analysis, group representations and applications
Additional book information: North-Holland, Amsterdam, 1992, vii+453 pp., $128.50. ISBN 0444 886 125.

Jeff Angel, Nancy Celniker, Steve Poulos, Audrey Terras, Cindy Trimble, and Elinor Velasquez, Special functions on finite upper half planes, Hypergeometric functions on domains of positivity, Jack polynomials, and applications (Tampa, FL, 1991) Contemp. Math., vol. 138, Amer. Math. Soc., Providence, RI, 1992, pp. 1–26. MR 1199118, DOI 10.1090/conm/138/1199118

[2]

J. Angel, S. Poulos, A. Terras, C. Trimble, and E. Velasquez, Spherical functions and transforms on finite upper half planes: chaotic pictures, uncertainty, traces, preprint.

James Arthur, The trace formula and Hecke operators, Number theory, trace formulas and discrete groups (Oslo, 1987) Academic Press, Boston, MA, 1989, pp. 11–27. MR 993309

Frédéric Bien, Constructions of telephone networks by group representations, Notices Amer. Math. Soc. 36 (1989), no. 1, 5–22. MR 972207

Ethan D. Bolker, The finite Radon transform, Integral geometry (Brunswick, Maine, 1984) Contemp. Math., vol. 63, Amer. Math. Soc., Providence, RI, 1987, pp. 27–50. MR 876312, DOI 10.1090/conm/063/876312

Fan R. K. Chung, Constructing random-like graphs, Probabilistic combinatorics and its applications (San Francisco, CA, 1991) Proc. Sympos. Appl. Math., vol. 44, Amer. Math. Soc., Providence, RI, 1991, pp. 21–55. MR 1141922, DOI 10.1090/psapm/044/1141922

Persi Diaconis, Group representations in probability and statistics, Institute of Mathematical Statistics Lecture Notes—Monograph Series, vol. 11, Institute of Mathematical Statistics, Hayward, CA, 1988. MR 964069

David L. Donoho and Philip B. Stark, Uncertainty principles and signal recovery, SIAM J. Appl. Math. 49 (1989), no. 3, 906–931. MR 997928, DOI 10.1137/0149053

[9]

J. R. Driscoll and D. M. Healy, Jr., Computing Fourier transforms and convolutions on the 2-sphere, preprint.

Donald Greenspan, Discrete models, Applied Mathematics and Computation, No. 3, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1973. MR 0366132

Martin C. Gutzwiller, Chaos in classical and quantum mechanics, Interdisciplinary Applied Mathematics, vol. 1, Springer-Verlag, New York, 1990. MR 1077246, DOI 10.1007/978-1-4612-0983-6

Sigurđur Helgason, Lie groups and symmetric spaces, Battelle Rencontres. 1967 Lectures in Mathematics and Physics, Benjamin, New York, 1968, pp. 1–71. MR 0236325

A. Lubotzky, R. Phillips, and P. Sarnak, Ramanujan graphs, Combinatorica 8 (1988), no. 3, 261–277. MR 963118, DOI 10.1007/BF02126799

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F. J. MacWilliams and N. J. A. Sloane, The theory of error-correcting codes, North Holland, Amsterdam, 1988.

Amar Mukhopadhyay (ed.), Recent developments in switching theory, Academic Press, New York-London, 1971. MR 0278844

Yôichirô Nambu, Field theory of Galois fields, Quantum field theory and quantum statistics, Vol. 1, Hilger, Bristol, 1987, pp. 625–636. MR 943162

Ilya Piatetski-Shapiro, Complex representations of $\textrm {GL}(2,\,K)$ for finite fields $K$, Contemporary Mathematics, vol. 16, American Mathematical Society, Providence, R.I., 1983. MR 696772

Audrey Terras, Harmonic analysis on symmetric spaces and applications. I, Springer-Verlag, New York, 1985. MR 791406, DOI 10.1007/978-1-4612-5128-6

[19]

-, Fourier analysis on finite groups and applications, Univ. of California, San Diego Lecture Notes.

[20]

E. Velasquez, Ph.D. thesis, Univ. of California, San Diego, 1991.

D. I. Wallace, The Selberg trace formula for $\textrm {SL}(3,\textbf {Z})\backslash \textrm {SL}(3,\textbf {R})/\textrm {SO}(3,\textbf {R})$, Trans. Amer. Math. Soc. 345 (1994), no. 1, 1–36. MR 1184117, DOI 10.1090/S0002-9947-1994-1184117-4

[1]

J. Angel, N. Celniker, S. Poulos, A. Terras, C. Trimble, and E. Velasquez, Special functions on finite upper half planes, Contemp. Math., vol. 138, Amer. Math. Soc., Providence, RI, 1992, pp. 1-26. MR 1199118 (94h:11041)

[2]

J. Angel, S. Poulos, A. Terras, C. Trimble, and E. Velasquez, Spherical functions and transforms on finite upper half planes: chaotic pictures, uncertainty, traces, preprint.

[3]

J. Arthur, The trace formula and Hecke operators, Number Theory, Trace Formulas, and Discrete Groups (K. E. Aubert et al., eds.), Academic Press, Boston, MA, 1989, pp. 11-27. MR 993309 (90e:11072)

[4]

F. Bien, Construction of telephone networks by group representations, Notices Amer. Math. Soc. 36 (1989), 187-196. MR 972207 (90a:90052)

[5]

E. D. Bolker, The finite Radon transform, Contemp. Math., vol. 63, Amer. Math. Soc., Providence, RI, 1987, pp. 27-50. MR 876312 (88b:51009)

[6]

F. Chung, Constructing random-like graphs, Proc. Sympos. Appl. Math., vol. 44, Amer. Math. Soc., Providence, RI, 1991, pp. 21-55. MR 1141922 (92m:05169)

[7]

P. Diaconis, Group representations in probability and statistics, Inst. Math. Statistics, Hayward, CA, 1988. MR 964069 (90a:60001)

[8]

D. L. Donoho and P. B. Stark, Uncertainty principles and signal recovery, SIAM J. Applied Math. 49 (1989), 906-931. MR 997928 (90c:42003)

[9]

J. R. Driscoll and D. M. Healy, Jr., Computing Fourier transforms and convolutions on the 2-sphere, preprint.

[10]

D. Greenspan, Discrete models, Addison-Wesley, Reading, MA, 1973. MR 0366132 (51:2382)

[11]

M. C. Gutzwiller, Chaos in classical and quantum mechanics, Springer-Verlag, New York, 1990. MR 1077246 (91m:58099)

[12]

S. Helgason, Lie groups and symmetric spaces, Battelle Recontres (C. M. DeWitt and J. A. Wheeler, eds.), Benjamin, New York, 1968, pp. 1-71. MR 0236325 (38:4622)

[13]

A Lubotsky, R. Phillips, and P. Sarnak, Ramanujan graphs, Combinatorica 8 (1988), 261-277. MR 963118 (89m:05099)

[14]

F. J. MacWilliams and N. J. A. Sloane, The theory of error-correcting codes, North Holland, Amsterdam, 1988.

[15]

A. Mukhopadhyay (ed.), Recent developments in switching theory, Academic Press, New York, 1971. MR 0278844 (43:4572)

[16]

Y. Nambu, Field theory of Galois fields, Quantum Field Theory and Quantum Statistics. I (I. A. Batalin et al., eds.), Hilger, Bristol, 1987, pp. 625-636. MR 943162 (90a:81154)

[17]

I. I. Piatetski-Shapiro, Complex representations of for finite fields K, Contemp. Math., vol. 16, Amer. Math. Soc., Providence, RI, 1983. MR 696772 (84m:20046)

[18]

A. Terras, Harmonic analysis on symmetric spaces and applications. I, II, Springer-Verlag, New York, 1985, 1988. MR 791406 (87f:22010)

[19]

-, Fourier analysis on finite groups and applications, Univ. of California, San Diego Lecture Notes.

[20]

E. Velasquez, Ph.D. thesis, Univ. of California, San Diego, 1991.

[21]

D. I. Wallace, The Selberg trace formula for , Trans. Amer. Math. Soc. (to appear). MR 1184117 (95a:11049)