Remarks on global hypoellipticity

Greenfield, Stephen J.; Wallach, Nolan R.

doi:10.1090/S0002-9947-1973-0400313-1

Remarks on global hypoellipticity
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by Stephen J. Greenfield and Nolan R. Wallach PDF

Trans. Amer. Math. Soc. 183 (1973), 153-164 Request permission

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.

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