On self-adjointness of a Schrödinger operator

on differential forms

Author:
Maxim Braverman

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

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Abstract: Let be a complete Riemannian manifold and let denote the space of differential forms on . Let be the exterior differential operator and let be the Laplacian. We establish a sufficient condition for the Schrödinger operator (where the potential 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.

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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

Email:
maxim@math.ohio-state.edu

DOI:
https://doi.org/10.1090/S0002-9939-98-04284-1

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

Article copyright:
© Copyright 1998
American Mathematical Society