Harmonic Analysis

The following sources are recommended by a professor whose research specialty is harmonic analysis.

Six Superlative Sources

· Harish-Chandra, "Spherical functions on a semi-simple Lie group, I and II," Amer. J. Math., Vol. 80 (1958), pp. 241-310 and 553-613.

· A.A. Kirillov, Elements of the theory of representations, Springer-Verlag, 1976.

· G. Mackey, "Harmonic analysis as the exploitation of symmetry--a historical survey," Bull. Amer. Math. Soc. (N.S.), Vol.3 (1980), pp. 543-698.

· E. Titchmarsh, Introduction to the theory of Fourier integrals, Chelsea Publishing, 1986.

· N. Vilenkin, Special functions and the theory of group representations, Amer. Math. Soc., 1968.

· A. Zygmund, Trigonometric series, Cambridge University Press, 1959.

Other Excellent Sources

· R. Askey, Orthogonal polynomials and special functions, SIAM, 1975.

· B. Berndt, ed., Ramanujan's notebooks, Springer, 1985.

· H. Ding and K. Gross, "Ramanujan's master theorem for symmetric cones," Pacific J. Math., Vol. 175 (1996), No. 2, pp. 447-490.

· J. Faraut and A. Korányi, Analysis on symmetric cones, Oxford, 1994.

· S.G. Gindikin, "Analysis in homogeneous domains," Russian Math. Surveys, Vol. 19 (1964), pp. 1-90.

· K. Gross, "On the evolution of noncommutative harmonic analysis," Amer. Math. Monthly, Vol. 85 (1978), pp. 525-548.

· K. Gross and R. Kunze, "Bessel functions and representation theory," J. Func. Anal., Vol. 22 (1976), pp. 73-105.

· K. Gross and D. Richards, "Special functions of matrix argument. I: Algebraic induction, zonal polynomials and hypergeometric functions," Trans. Amer. Math. Soc., Vol. 301 (1987), pp. 781-811.

· G.H. Hardy, Ramanujan: Twelve lectures on subjects suggested by his life and work, AMS Chelsea, 1999.

· Harish-Chandra, "Harmonic analysis on semisimple Lie groups," Bull. Amer. Math. Soc., Vol. 76 (1970), pp. 529-551.

· S. Helgason, Differential geometry, Lie groups, and symmetric spaces, Amer. Math. Soc., 2001.

· S. Helgason, Groups and geometric analysis, Academic Press, 1984.

· R. Howe, "Remarks on classical invariant theory," Trans. Amer. Math. Soc., Vol. 313 (1989), pp. 539-570.

· L.K. Hua, Harmonic analysis of functions of several variables in the classical domains, Amer. Math. Soc., 1963.

· A.W. Knapp, Representation theory of semisimple groups: An overview based on examples, Princeton University Press, 1986.

· M. Koecher, The Minnesota notes on Jordan algebras and their applications, Springer, 1999.

· I.G. Macdonald, Symmetric functions and Hall polynomials, Clarendon Press, 1995.

· W. Rudin, Fourier analysis on groups, Interscience, 1962.

· E. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton University Press, 1975.

· N. Wallach, Harmonic analysis on homogeneous spaces, Marcel Dekker, 1973.

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