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Differential equations and an analog of the Paley-Wiener theorem for linear semisimple Lie groups

Published online by Cambridge University Press:  22 January 2016

Kenneth D. Johnson
Kenneth D. Johnson*
Affiliation:
Department of Mathematics Indiana University
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Let G be a noncompact linear semisimple Lie group. Fix G = KAN an Iwasawa decomposition of G. That is, K is a maximal compact subgroup of G, A is a vector subgroup with AdA consisting of semisimple transformations and A normalizes N, a simply connected nilpotent subgroup of G.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 64 , December 1976 , pp. 17 - 29
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1976

References

[1] Arthur, J., Harmonic analysis of the Schwartz space on a reductive Lie group II, preprint.Google Scholar
[2] Ehrenpreis, L. and Mautner, F., Some properties of the Fourier transform on semisimple Lie groups, I, Ann. of Math. 61 (1955), 406–439.Google Scholar
[3] Gangolli, R., On the Plancherel formula and the Paley-Wiener theorem for spherical functions on semisimple Lie groups, Ann. of Math. 93 (1971), 150–165.Google Scholar
[4] Gindikin, S. G. and Karpelevic, F. I., Plancherel measure of Riemannian symmetric spaces of nonpositive curvature, Sov. Math. 3 (1962), 962–965.Google Scholar
[5] Harish-Chandra, , Discrete series for semisimple Lie groups II, Acta. Math. 116 (1966), 1–111.CrossRefGoogle Scholar
[6] Harish-Chandra, , On the theory of the Eisenstein integral, Proc. Int. Conf. on Harm. Anal., Univ. of Maryland, 1971, lecture notes in Math. No. 266, Springer-Verlag, 1972.Google Scholar
[7] Harish-Chandra, , Lectures at Institute for Advanced Study, Fall 1974.Google Scholar
[8] Helgason, S., An analog of the Paley-Wiener theorem for the Fourier transform on certain symmetric spaces, Math. Ann. 165 (1966), 297–308.Google Scholar
[9] Helgason, S., A duality for symmetric spaces, with applications to group representations, Advan. Math. 5 (1970), 1–154.Google Scholar
[10] Helgason, S., The surjectivity of invariant differential operators on symmetric spaces I, Ann. of Math. 98 (1973), 451–479.CrossRefGoogle Scholar
[11] Hormander, L., Linear partial differential operators, Springer-Verlag, 1963.Google Scholar
[12] Johnson, K., Functional analysis on SU (1,1), Advan. Math. 14 (1974), 346–364.Google Scholar
[13] Johnson, K., Paley-Wiener theorems on groups of split rank one, to appear.Google Scholar
[14] Johnson, K., Partial differential equations on semisimple Lie groups, to appear. Google Scholar
[15] Schiffmann, G., Integrales d’entrelacement et fonctions de Whittaker, Bull. Soc. Math. France 99 (1971), 3–72.CrossRefGoogle Scholar
[16] Warner, G., Harmonic analysis on semisimple Lie groups, Springer-Verlag, 1972.Google Scholar