Remarks on Global Hypoellipticity
Open Access
- 1 September 1973
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 183, 153-164
- https://doi.org/10.2307/1996464
Abstract
We study differential operators D which commute with a fixed normal elliptic operator E on a compact manifold M. We use eigenfunction expansions relative to E to obtain simple conditions giving global hypoellipticity. These conditions are equivalent to D having parametrices in certain spaces of functions or distributions. An example is given by M = compact Lie group and and E = Casimir operator, with D any invariant differential operator. The connections with global subelliptic estimates are investigated.Keywords
This publication has 7 references indexed in Scilit:
- Globally hypoelliptic vector fieldsTopology, 1973
- Hypoelliptic Vector Fields and Continued FractionsProceedings of the American Mathematical Society, 1972
- Global Hypoellipticity and Liouville NumbersProceedings of the American Mathematical Society, 1972
- Eigenfunction Expansions of Analytic FunctionsProceedings of the American Mathematical Society, 1969
- Hypoelliptic second order differential equationsActa Mathematica, 1967
- Integro-Differential Operators on Vector BundlesTransactions of the American Mathematical Society, 1965
- An Invariant Criterion of HypoellipticityAmerican Journal of Mathematics, 1961