Solvability of noninvariant differential operators on homogeneous spaces
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- by Ronald L. Lipsman PDF
- Proc. Amer. Math. Soc. 107 (1989), 271-276 Request permission
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.References
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Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 107 (1989), 271-276
- MSC: Primary 22E99; Secondary 43A85, 58G99
- DOI: https://doi.org/10.1090/S0002-9939-1989-0979228-3
- MathSciNet review: 979228