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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Solvability of noninvariant differential operators on homogeneous spaces


Author: Ronald L. Lipsman
Journal: Proc. Amer. Math. Soc. 107 (1989), 271-276
MSC: Primary 22E99; Secondary 43A85, 58G99
MathSciNet review: 979228
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Abstract: We consider the solvability of non-invariant differential operators on homogeneous spaces. Such operators cannot be expected to have solutions in smooth functions (an illustrative example is provided). However, Lion has shown that, under suitable growth conditions on the infinitesimal components of the operators in a representation-theoretic decomposition, one can deduce solvability in a space of distributions. In this paper we prove that Lion's result can be improved to yield solvability in square-integrable functions.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0979228-3
PII: S 0002-9939(1989)0979228-3
Article copyright: © Copyright 1989 American Mathematical Society