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Proceedings of the American Mathematical Society
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0447830-4
PII: S 0002-9939(1976)0447830-4
Keywords: Partial differential operators, essential selfadjointness, quasi-analytic vectors
Article copyright: © Copyright 1976 American Mathematical Society