A new interpolation formula for the Titchmarsh-Weyl -function

Authors:
Alexei Rybkin and Vu Kim Tuan

Journal:
Proc. Amer. Math. Soc. **137** (2009), 4177-4185

MSC (2000):
Primary 47E05, 65D05

DOI:
https://doi.org/10.1090/S0002-9939-09-09983-3

Published electronically:
June 25, 2009

MathSciNet review:
2538578

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For the Titchmarsh-Weyl -function of the half-line Schrödinger operator with Dirichlet boundary conditions we put forward a new interpolation formula which allows one to reconstruct the -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:
https://doi.org/10.1090/S0002-9939-09-09983-3

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