Transactions of the American Mathematical Society

Author(s): Miklós Horváth
Journal: Trans. Amer. Math. Soc. 353 (2001), 4155-4171.
MSC (1991): Primary 34A55, 34B20; Secondary 34L40, 47A75
Posted: May 17, 2001
Retrieve article in: PDF
This article is available free of charge

We prove that under some conditions finitely many partially known spectra and partial information on the potential entirely determine the potential. This extends former results of Hochstadt, Lieberman, Gesztesy, Simon and others.

1.: G. Borg, Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe, Acta Math. 78 (1946), 1-96. MR 7:382d
2.: G. Borg, Uniqueness theorems in the spectral theory of $y''+(\lambda-q(x))y=0$ , Proc. 11th Scandinavian Congress of Mathematicians, Johan Grundt Tanums Forlag, Oslo, 1952, pp. 276-287. MR 15:315a
3.: F. Gesztesy, R. del Rio and B. Simon, Inverse spectral analysis with partial information on the potential, III. Updating boundary conditions, Intl. Math. Research Notices 15 (1997), 751-758. MR 99a:34032
4.: F. Gesztesy, R. del Rio and B. Simon, Corrections and Addendum to ``Inverse spectral analysis with partial information on the potential, III. Updating boundary conditions'', Intl. Math. Research Notices 11 (1999), 623-625. MR 2000d:34025
5.: F. Gesztesy and B. Simon, Inverse spectral analysis with partial information on the potential, II. The case of discrete spectrum, Trans. Amer. Math. Soc. 352 (2000), 2765-2787. MR 2000j:34019
6.: F. Gesztesy and B. Simon, On the determination of the potential from three spectra, Trans. Amer. Math. Soc. 189(2) (1999), 85-92. MR 2000i:34026
7.: H. Hochstadt and B. Lieberman, An inverse Sturm-Liouville problem with mixed given data, SIAM J. Appl. Math. 34 (1978), 676-680. MR 57:10077
8.: N. Levinson, Gap and density theorems, AMS Coll. Publ., 1940, New York. MR 2:180d
9.: B. M. Levitan and I. S. Sargsjan, Sturm-Liouville and Dirac operators (in Russian), Nauka, Moscow 1988; English transl. MR 92i:34119
10.: B. M. Levitan and I. S. Sargsjan, Introduction to spectral theory (in Russian), Nauka, Moscow 1970. MR 33:4362
11.: B. Ja. Levin, Distribution of zeros of entire functions (in Russian), GITTL, Moscow 1956. MR 19:402c
12.: V.A. Marchenko, Certain problems in the theory of second order differential operators (in Russian), Dokl. Akad. Nauk. SSSR, 72 (1950), 457-460.
13.: B.A. Watson, Inverse spectral problems for weighted Dirac systems, Inverse Problems, 15(3) (1999), 793-805. MR 2000d:34184

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 34A55, 34B20, 34L40, 47A75

Miklós Horváth
Affiliation: Budapest University of Technology and Economics, Institute of Mathematics, H 1111 Budapest, Muegyetem rkp. 3-9, Hungary
Email: horvath@math.bme.hu

DOI: 10.1090/S0002-9947-01-02765-9
PII: S 0002-9947(01)02765-9
Keywords: Inverse spectral theory, $m$-function, spectral function
Received by editor(s): February 16, 2000
Received by editor(s) in revised form: June 7, 2000
Posted: May 17, 2001
Additional Notes: Research supported by the Hungarian NSF Grant OTKA T\#32374
Copyright of article: Copyright 2001, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6850(e) ISSN 0002-9947(p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS