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On the Two Spectra Inverse Problem for Semi-infinite Jacobi Matrices

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Abstract

We present results on the unique reconstruction of a semi-infinite Jacobi operator from the spectra of the operator with two different boundary conditions. This is the discrete analogue of the Borg–Marchenko theorem for Schrödinger operators on the half-line. Furthermore, we give necessary and sufficient conditions for two real sequences to be the spectra of a Jacobi operator with different boundary conditions.

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Authors and Affiliations

  1. Departamento de Métodos Matemáticos y Numéricos, Instituto de Investigaciones, en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, México, D.F. C.P. 04510, Mexico

    Luis O. Silva & Ricardo Weder

  2. IIMAS Universidad Nacional Autónoma de México, Apartado Postal 20-726, México, D.F. 01000, Mexico

    Ricardo Weder

Authors
  1. Luis O. Silva
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  2. Ricardo Weder
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Correspondence to Ricardo Weder.

Additional information

Research partially supported by Universidad Nacional Autónoma de México under Project PAPIIT-DGAPA IN 105799, and by CONACYT under Project P42553F.

R. Weder is a fellow of Sistema Nacional de Investigadores.

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Silva, L.O., Weder, R. On the Two Spectra Inverse Problem for Semi-infinite Jacobi Matrices. Math Phys Anal Geom 9, 263–290 (2006). https://doi.org/10.1007/s11040-007-9014-7

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