Essential selfadjointness of certain partial differential operators on $R^{n}$
HTML articles powered by AMS MathViewer
- by A. Devinatz PDF
- Proc. Amer. Math. Soc. 60 (1976), 235-242 Request permission
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.References
- Paul R. Chernoff, Essential self-adjointness of powers of generators of hyperbolic equations, J. Functional Analysis 12 (1973), 401–414. MR 0369890, DOI 10.1016/0022-1236(73)90003-7
- A. E. Nussbaum, Quasi-analytic vectors, Ark. Mat. 6 (1965), 179–191 (1965). MR 194899, DOI 10.1007/BF02591357
- A. E. Nussbaum, A note on quasi-analytic vectors, Studia Math. 33 (1969), 305–309. MR 251554, DOI 10.4064/sm-33-3-305-309
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 60 (1976), 235-242
- MSC: Primary 35P05; Secondary 47F05
- DOI: https://doi.org/10.1090/S0002-9939-1976-0447830-4
- MathSciNet review: 0447830