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.

Full Text

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},
}