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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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  • [1] Paul R. Chernoff, Essential self-adjointness of powers of generators of hyperbolic equations, J. Functional Analysis 12 (1973), 401-414. MR 0369890 (51:6119)
  • [2] A. E. Nussbaum, Quasi-analytic vectors, Ark. Mat. 6 (1965), 179-191. MR 33 #3105. MR 0194899 (33:3105)
  • [3] -, A note on quasi-analytic vectors, Studia Math. 33 (1969), 305-309. MR 40 #4781. MR 0251554 (40:4781)

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

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