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

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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.

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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

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  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 CONACYT under Project P42553F.

L. O. Silva partially supported by PAPIIT-UNAM through grant IN-111906.

Ricardo Weder is a fellow of Sistema Nacional de Investigadores.

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Silva, L.O., Weder, R. The Two-Spectra Inverse Problem for Semi-infinite Jacobi Matrices in The Limit-Circle Case. Math Phys Anal Geom 11, 131–154 (2008). https://doi.org/10.1007/s11040-008-9044-9

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  • DOI: https://doi.org/10.1007/s11040-008-9044-9

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