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Proceedings of the American Mathematical Society

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



Essential selfadjointness of certain partial differential operators on $ R\sp{n}$

Author: A. Devinatz
Journal: Proc. Amer. Math. Soc. 60 (1976), 235-242
MSC: Primary 35P05; Secondary 47F05
MathSciNet review: 0447830
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Abstract: Sufficient conditions are given on the coefficients of a second order, semibounded, formally selfadjoint differential operator on $ {R^n}$, not necessarily elliptic, so that the closure of the operator restricted to $ C_0^\infty ({R^n})$ is selfadjoint. The results are based on A. E. Nussbaum's notion of quasi-analytic vectors.

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Keywords: Partial differential operators, essential selfadjointness, quasi-analytic vectors
Article copyright: © Copyright 1976 American Mathematical Society