The Two-Spectra Inverse Problem for Semi-Infinite Jacobi Matrices in The
  Limit-Circle Case

B. Simon; B. Simon; B.M. Brown; B.M. Levitan; D. Chelkak; F. Gesztesy; F. Gesztesy; F. Gesztesy; G. Borg; G. Teschl; G. Teschl; G.Š. Guseĭnov; J.M. Berezans′kiĭ; L. Fu; L.O. Silva; L.V. Ahlfors; Luis O. Silva; M. Kreĭn; M.G. Gasymov; M.G. Gasymov; M.G. Kreĭn; M.G. Kreĭn; M.G. Kreĭn; M.L. Gorbachuk; N.I. Akhiezer; N.I. Akhiezer; R. Weikard; R.Z. Halilova; Ricardo Weder; S. Albeverio; T. Aktosun; T. Aktosun; V.A. Marčenko; W.F. Donoghue Jr.

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The Two-Spectra Inverse Problem for Semi-Infinite Jacobi Matrices in The Limit-Circle Case

Authors: B. Simon
B. Simon
B.M. Brown
B.M. Levitan
D. Chelkak
F. Gesztesy
F. Gesztesy
F. Gesztesy
G. Borg
G. Teschl
G. Teschl
G.Š. Guseĭnov
J.M. Berezans′kiĭ
L. Fu
L.O. Silva
L.V. Ahlfors
Luis O. Silva
M. Kreĭn
M.G. Gasymov
M.G. Gasymov
M.G. Kreĭn
M.G. Kreĭn
M.G. Kreĭn
M.L. Gorbachuk
N.I. Akhiezer
N.I. Akhiezer
R. Weikard
R.Z. Halilova
Ricardo Weder
S. Albeverio
T. Aktosun
T. Aktosun
V.A. Marčenko
W.F. Donoghue Jr.
Publication date: 12 September 2008
Publisher: 'Springer Science and Business Media LLC'
Doi

Abstract

We present a technique for reconstructing a semi-infinite Jacobi operator in the limit circle case from the spectra of two different self-adjoint extensions. Moreover, we give necessary and sufficient conditions for two real sequences to be the spectra of two different self-adjoint extensions of a Jacobi operator in the limit circle case.Comment: 26 pages. Changes in the presentation of some result

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