Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Remarks on global hypoellipticity

Authors: Stephen J. Greenfield and Nolan R. Wallach
Journal: Trans. Amer. Math. Soc. 183 (1973), 153-164
MSC: Primary 58G15; Secondary 35H05
MathSciNet review: 0400313
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 58G15, 35H05

Retrieve articles in all journals with MSC: 58G15, 35H05

Additional Information

Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society