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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A new interpolation formula for the Titchmarsh-Weyl $ m$-function


Authors: Alexei Rybkin and Vu Kim Tuan
Journal: Proc. Amer. Math. Soc. 137 (2009), 4177-4185
MSC (2000): Primary 47E05, 65D05
Published electronically: June 25, 2009
MathSciNet review: 2538578
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Abstract: For the Titchmarsh-Weyl $ m$-function of the half-line Schrödinger operator with Dirichlet boundary conditions we put forward a new interpolation formula which allows one to reconstruct the $ m$-function from its values on a certain infinite set of points for a broad class of potentials.


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Additional Information

Alexei Rybkin
Affiliation: Department of Mathematics and Statistics, University of Alaska Fairbanks, P.O. Box 756660, Fairbanks, Alaska 99775
Email: ffavr@uaf.edu

Vu Kim Tuan
Affiliation: Department of Mathematics, University of West Georgia, Carrollton, Georgia 30118
Email: vu@westga.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09983-3
PII: S 0002-9939(09)09983-3
Keywords: Titchmarsh-Weyl $m$-function, interpolation, $A$-amplitude, Hardy space
Received by editor(s): October 28, 2008
Received by editor(s) in revised form: April 2, 2009
Published electronically: June 25, 2009
Additional Notes: This research was supported in part by the U.S. National Science Foundation under grant DMS 070747
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2009 American Mathematical Society