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Bochner identities for Fourier transforms. (English) Zbl 0349.43007


MSC:

43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
43A65 Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis)
43A85 Harmonic analysis on homogeneous spaces
22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
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[1] S. Bochner, Theta relations with spherical harmonics, Proc. Nat. Acad. Sci. U. S. A. 37 (1951), 804 – 808. · Zbl 0044.07501
[2] Hermann Boerner, Representations of groups. With special consideration for the needs of modern physics, Translated from the German by P. G. Murphy in cooperation with J. Mayer-Kalkschmidt and P. Carr. Second English edition, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1970. · Zbl 0167.02601
[3] Stephen S. Gelbart, A theory of Stiefel harmonics, Trans. Amer. Math. Soc. 192 (1974), 29 – 50. · Zbl 0292.22016
[4] Harish-Chandra, Differential operators on a semisimple Lie algebra, Amer. J. Math. 79 (1957), 87 – 120. · Zbl 0072.01901
[5] G. C. Hegerfeldt, Branching theorem for the symplectic groups, J. Mathematical Phys. 8 (1967), 1195 – 1196. · Zbl 0189.32303
[6] SigurĂ„’ur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962.
[7] Carl S. Herz, Bessel functions of matrix argument, Ann. of Math. (2) 61 (1955), 474 – 523. · Zbl 0066.32002
[8] Robert S. Strichartz, The explicit Fourier decomposition of \?²(\?\?(\?)/\?\?(\?-\?)), Canad. J. Math. 27 (1975), 294 – 310. · Zbl 0275.43009
[9] Robert S. Strichartz, Fourier transforms and non-compact rotation groups, Indiana Univ. Math. J. 24 (1974/75), 499 – 526. · Zbl 0295.42015
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