Partial differential equations on semisimple Lie groups

Author:
Kenneth D. Johnson

Journal:
Proc. Amer. Math. Soc. **60** (1976), 289-295

MSC:
Primary 22E30; Secondary 43A85

MathSciNet review:
0425016

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Abstract: Suppose *G* is a noncompact, connected, semisimple Lie group with finite center and *K* is a maximal compact subgroup. Let *D* be an Ad *K*invariant element in the complexified enveloping algebra of *G*. The main result of this paper gives criterion for when the map is injective, where is the space of compactly supported distributions on *G*.

**[1]**Harish-Chandra,*Spherical functions on a semisimple Lie group. I*, Amer. J. Math.**80**(1958), 241–310. MR**0094407****[2]**Harish-Chandra,*Spherical functions on a semisimple Lie group. II*, Amer. J. Math.**80**(1958), 553–613. MR**0101279****[3]**Harish-Chandra,*Discrete series for semisimple Lie groups. II. Explicit determination of the characters*, Acta Math.**116**(1966), 1–111. MR**0219666****[4]**Harish-Chandra,*On the theory of the Eisenstein integral*, Conference on Harmonic Analysis (Univ. Maryland, College Park, Md., 1971), Springer, Berlin, 1972, pp. 123–149. Lecture Notes in Math., Vol. 266. MR**0399355****[5]**Sigurdur Helgason,*The surjectivity of invariant differential operators on symmetric spaces. I*, Ann. of Math. (2)**98**(1973), 451–479. MR**0367562****[6]**Kenneth D. Johnson,*Differential equations and an analog of the Paley-Wiener theorem for linear semisimple Lie groups*, Nagoya Math. J.**64**(1976), 17–29. MR**0480876**

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1976-0425016-7

Article copyright:
© Copyright 1976
American Mathematical Society