Damanik, David and Killip, Rowan and Simon, Barry (2004) Necessary and Sufficient Conditions in the Spectral Theory of Jacobi Matrices and Schrödinger Operators. International Mathematics Research Notices, 2004 (22). pp. 1087-1097. ISSN 1073-7928. doi:10.1155/S1073792804132790. https://resolver.caltech.edu/CaltechAUTHORS:20110920-104550878
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Abstract
We announce three results in the theory of Jacobi matrices and Schrödinger operators. First, we give necessary and sufficient conditions for a measure to be the spectral measure of a Schrödinger operator −d^2/dx^2+V(x) on L^2 (0,∞) with V ∈ L2(0,∞) and the boundary condition u(0) = 0. Second, we give necessary and sufficient conditions on the Jacobi parameters for the associated orthogonal polynomials to have Szegő asymptotics. Finally, we provide necessary and sufficient conditions on a measure to be the spectral measure of a Jacobi matrix with exponential decay at a given rate.
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| Additional Information: | © 2004 Hindawi Publishing Corporation. Received September 11, 2003. Revision received December 3, 2003. Accepted January 29, 2004. We would like to thank Roman Romanov for drawing our attention to [9]. David Damanik was supported in part by National Science Foundation (NSF) Grant DMS-0227289, and Barry Simon was supported in part by NSF Grant DMS-0140592. | |||||||||
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| Issue or Number: | 22 | |||||||||
| DOI: | 10.1155/S1073792804132790 | |||||||||
| Record Number: | CaltechAUTHORS:20110920-104550878 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20110920-104550878 | |||||||||
| Official Citation: | David Damanik, Rowan Killip, and Barry Simon Necessary and sufficient conditions in the spectral theory of Jacobi matrices and Schrödinger operators Int Math Res Notices (2004) Vol. 2004 1087-1097 doi:10.1155/S1073792804132790 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 25365 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 20 Sep 2011 20:05 | |||||||||
| Last Modified: | 09 Nov 2021 16:32 |
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