Published November 1, 1996
| Version public
Journal Article
A Trace Formula for Multidimensional Schrödinger Operators
Creators
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1.
University of Missouri
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2.
Norwegian University of Science and Technology
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3.
California Institute of Technology
Abstract
We prove multidimensional analogs of the trace formula obtained previously for one-dimensional Schrödinger operators. For example, letVbe a continuous function on [0, 1]^ν⊂R^ν. For A⊂{1,…,ν}, let −Δ_A be the Laplace operator on [0, 1]^ν with mixed Dirichlet–Neumann boundary conditions[formula]Let |A|= number of points inA. Then we'll prove that[formula]with ⦠V⦔ the average of Vat the 2^ν corners of [0, 1]^ν.
Additional Information
© 1996 Academic Press, Inc. Received 7 April 1995. This material is based upon work supported by the National Science Foundation under Grant No. DMS-9101715. The Government has certain rights in this material. We thank Peter Lax for telling us of his work prior to publication. F. G. is indebted to M. Aschbacher and G. Neugebauer for the hospitality at Caltech where some of this work was done. F. G. and H. H. were also supported in part by the Norwegian Research Council for Science and the Humanities (NAVF).Additional details
Identifiers
- Eprint ID
- 81345
- DOI
- 10.1006/jfan.1996.0137
- Resolver ID
- CaltechAUTHORS:20170912-095106346
Related works
- Describes
- 10.1006/jfan.1996.0137 (DOI)
Funding
- NSF
- DMS-9101715
- Norwegian Research Council for Science and the Humanities
Dates
- Created
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2017-09-12Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field
Caltech Custom Metadata
- Caltech groups
- Mathematics Department , Physics Department