|
A new interpolation formula for the Titchmarsh-Weyl  -function
Author(s):
Alexei
Rybkin;
Vu
Kim
Tuan
Journal:
Proc. Amer. Math. Soc.
137
(2009),
4177-4185.
MSC (2000):
Primary 47E05, 65D05
Posted:
June 25, 2009
MathSciNet review:
2538578
Retrieve article in:
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.
References:
-
- 1.
- J. Agler and J. E. McCarthy. Pick Interpolation and Hilbert Function Spaces. Graduate Studies in Mathematics, 44. American Mathematical Society, Providence, RI, 2002. MR 1882259 (2003b:47001)
- 2.
- S. Avdonin, V. Mikhaylov, and A. Rybkin. The boundary control approach to the Titchmarsh-Weyl
 -function. I. The response operator and the  -amplitude. Comm. Math. Phys. 275 (2007), no. 3, pp. 791-803. MR 2336364 (2008g:93083) - 3.
- A. Boumenir and Vu Kim Tuan. The interpolation of the Titchmarsh-Weyl function. J. Math. Anal. Appl. 335 (2007), pp. 72-78. MR 2340306 (2008f:34059)
- 4.
- A. Boumenir and Vu Kim Tuan. Sampling eigenvalues in Hardy spaces. SIAM J. Numer. Anal. 45 (2007), no. 2, pp. 473-483. MR 2300282 (2008c:65180)
- 5.
- F. Gesztesy and B. Simon. A new approach to inverse spectral theory, II. General real potentials and the connection to the spectral measure. Ann. of Math. (2) 152 (2000), no. 2, pp. 593-643. MR 1804532 (2001m:34185b)
- 6.
- A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev. Integrals and Series. Special Functions (Russian). Nauka, Moscow, 1983, English translation: Integrals and series. Vol. 3. More special functions. Gordon and Breach Science Publishers, New York, 1990. MR 1054647 (91c:33001)
- 7.
- A. G. Ramm. Recovery of the potential from
 -function. C. R. Math. Rep. Acad. Sci. Canada 9 (1987), no. 4, pp. 177-182. MR 896977 (88k:34012) - 8.
- B. Simon. A new approach to inverse spectral theory, I. Fundamental formalism. Ann. of Math. (2) 150 (1999), no. 3, pp. 1029-1057. MR 1740987 (2001m:34185a)
- 9.
- P. K. Suetin. Classical Orthogonal Polynomials (Russian), Second edition. Nauka, Moscow, 1979. MR 548727 (80h:33001)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
47E05, 65D05
Retrieve articles in all Journals with
MSC (2000):
47E05, 65D05
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:
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
Posted:
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
Copyright of article:
Copyright
2009,
American Mathematical Society
|
