Schrödinger operators with a complex valued potential
Abstract: If is a compact Riemannian manifold for which , is a continuous complex valued function whose imaginary part is of constant sign, and for some complex valued function on , then either vanishes somewhere or there is a constant and an everywhere positive function such that .
- 1. K. Yano and S. Bochner, Curvature and Betti numbers, Annals of Mathematics Studies, No. 32, Princeton University Press, Princeton, N. J., 1953. MR 0062505
- 2. Sol Schwartzman, Schrödinger operators and the zeros of their eigenfunctions, Comm. Math. Phys. 306 (2011), no. 1, 187–191. MR 2819423, 10.1007/s00220-011-1272-3
Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 35J10
Retrieve articles in all journals with MSC (2010): 35J10
Affiliation: Department of Mathematics, University of Rhode Island, Kingston, Rhode Island 02881
Received by editor(s): May 19, 2011
Published electronically: April 4, 2012
Communicated by: Chuu-Lian Terng
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.