Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Global hypoellipticity of a Mathieu operator


Author: Masafumi Yoshino
Journal: Proc. Amer. Math. Soc. 111 (1991), 717-720
MSC: Primary 35H05; Secondary 58G99
MathSciNet review: 1042277
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Abstract: We give a necessary and sufficient condition for the global hypoellipticity of a Mathieu operator on the torus $ {\mathbb{T}^d}$ in terms of continued fractions. It is not hypoelliptic, nor does it satisfy a controllability condition, a Hörmander condition, or a Siegel condition. But it is still globally hypoelliptic (cf. [1, 3]).


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1042277-2
Keywords: Hypoellipticity, global hypoellipticity, continued fractions
Article copyright: © Copyright 1991 American Mathematical Society