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# Borg-type theorems for generalized Jacobi matrices and trace formulas

### Abstract

The paper deals with two types of inverse spectral problems for the class of generalized Jacobi matrices introduced in [9]. Following the scheme proposed in [5], we deduce analogs of the Hochstadt-Lieberman theorem and the Borg theorem. Properties of a Weyl function of the generalized Jacobi matrix are systematically used to prove the uniqueness theorems. Trace formulas for the generalized Jacobi matrix are also derived.

### Article Information

 Title Borg-type theorems for generalized Jacobi matrices and trace formulas Source Methods Funct. Anal. Topology, Vol. 12 (2006), no. 3, 220-233 MathSciNet MR2261576 Copyright The Author(s) 2006 (CC BY-SA)

### Authors Information

M. S. Derevyagin
Department of Mathematics, Donets'k National University, 24 Universitets'ka, Donets'k, 83055, Ukraine

### Citation Example

M. S. Derevyagin, Borg-type theorems for generalized Jacobi matrices and trace formulas, Methods Funct. Anal. Topology 12 (2006), no. 3, 220-233.

### BibTex

@article {MFAT353,
AUTHOR = {Derevyagin, M. S.},
TITLE = {Borg-type theorems for generalized Jacobi matrices and trace formulas},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {12},
YEAR = {2006},
NUMBER = {3},
PAGES = {220-233},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=353},
}