Transactions of the American Mathematical Society

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



Globally hypoelliptic and globally solvable first-order evolution equations

Author: Jorge Hounie
Journal: Trans. Amer. Math. Soc. 252 (1979), 233-248
MSC: Primary 35H05; Secondary 57R25, 58G05
MathSciNet review: 534120
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Abstract: We consider global hypoellipticity and global solvability of abstract first order evolution equations defined either on an interval or in the unit circle, and prove that it is equivalent to certain conditions bearing on the total symbol. We relate this to known results about hypoelliptic vector fields on the 2-torus.

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Keywords: Evolution operator, global hypoellipticity, global solvability
Article copyright: © Copyright 1979 American Mathematical Society