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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
DOI: https://doi.org/10.1090/S0002-9947-1973-0400313-1
MathSciNet review: 0400313
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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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DOI: https://doi.org/10.1090/S0002-9947-1973-0400313-1
Article copyright: © Copyright 1973 American Mathematical Society