Fourier inversion for semisimple Lie groups of real rank one

Sally, P. J., Jr.; Warner, Garth

doi:10.1090/S0002-9904-1972-12944-6

Authors: P. J. Sally Jr. and Garth Warner
Journal: Bull. Amer. Math. Soc. 78 (1972), 251-254
MSC (1970): Primary 22E30; Secondary 22D10, 43A30
DOI: https://doi.org/10.1090/S0002-9904-1972-12944-6
MathSciNet review: 0299733
Full-text PDF Free Access

Stephen S. Gelbart, Fourier analysis on matrix space, American Mathematical Society, Providence, R.I., 1971. Memoirs of the American Mathematical Society, No. 108. MR 0492066
I. M. Gel′fand, M. I. Graev, and I. I. Pjateckiĭ-Šapiro, Teoriya predstavleniĭ i avtomorfnye funktsii, Generalized functions, No. 6, Izdat. “Nauka”, Moscow, 1966 (Russian). MR 0220673
Harish-Chandra, A formula for semisimple Lie groups, Amer. J. Math. 79 (1957), 733–760. MR 96138, DOI https://doi.org/10.2307/2372432
Harish-Chandra, Harmonic analysis on semisimple Lie groups, Some Recent Advances in the Basic Sciences, Vol. 1 (Proc. Annual Sci. Conf., Belfer Grad. School Sci., Yeshiva Univ., New York, 1962-1964) Belfer Graduate School of Science, Yeshiva Univ., New York, 1966, pp. 35–40. MR 0210832
Harish-Chandra, Invariant differential operators and distributions on a semisimple Lie algebra, Amer. J. Math. 86 (1964), 534–564. MR 180628, DOI https://doi.org/10.2307/2373023
Harish-Chandra, Invariant differential operators and distributions on a semisimple Lie algebra, Amer. J. Math. 86 (1964), 534–564. MR 180628, DOI https://doi.org/10.2307/2373023
Harish-Chandra, Discrete series for semisimple Lie groups. I. Construction of invariant eigendistributions, Acta Math. 113 (1965), 241–318. MR 219665, DOI https://doi.org/10.1007/BF02391779
Harish-Chandra, Two theorems on semi-simple Lie groups, Ann. of Math. (2) 83 (1966), 74–128. MR 194556, DOI https://doi.org/10.2307/1970472
Harish-Chandra, Discrete series for semisimple Lie groups. II. Explicit determination of the characters, Acta Math. 116 (1966), 1–111. MR 219666, DOI https://doi.org/10.1007/BF02392813

4. P. J. Sally, Jr. and J. A. Shalika, The Fourier transform on SL(2) over a non-archimedean local field (to appear).

Garth Warner, Harmonic analysis on semi-simple Lie groups. I, Springer-Verlag, New York-Heidelberg, 1972. Die Grundlehren der mathematischen Wissenschaften, Band 188. MR 0498999