On self-adjointness of a Schrödinger operator on differential forms
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- by Maxim Braverman PDF
- Proc. Amer. Math. Soc. 126 (1998), 617-623 Request permission
Abstract:
Let $M$ be a complete Riemannian manifold and let $\Omega ^{\bullet }(M)$ denote the space of differential forms on $M$. Let $d:\Omega ^{\bullet }(M)\to \Omega ^{\bullet +1}(M)$ be the exterior differential operator and let $\Delta =dd^{*}+d^{*}d$ be the Laplacian. We establish a sufficient condition for the Schrödinger operator $H=\Delta +V(x)$ (where the potential $V(x):\Omega ^{\bullet }(M)\to \Omega ^{\bullet }(M)$ is a zero order differential operator) to be self-adjoint. Our result generalizes a theorem by I. Oleinik about self-adjointness of a Schrödinger operator which acts on the space of scalar valued functions.References
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Additional Information
- Maxim Braverman
- Affiliation: Department of Mathematics, Ohio State University, Columbus, Ohio 43210
- Address at time of publication: Department of Mathematics, The Hebrew University, Jerusalem 91904, Israel
- MR Author ID: 368038
- Email: maxim@math.ohio-state.edu
- Received by editor(s): August 19, 1996
- Additional Notes: The research was supported by US - Israel Binational Science Foundation grant No. 9400299
- Communicated by: Jeffrey B. Rauch
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 617-623
- MSC (1991): Primary 58G25; Secondary 35P05
- DOI: https://doi.org/10.1090/S0002-9939-98-04284-1
- MathSciNet review: 1443372