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Article Dans Une Revue Journal of Mathematical Physics Année : 2017

A point interaction for the discrete Schr\"odinger operator and generalized Chebyshev polynomials

Résumé

We consider semi-infinite Jacobi matrices corresponding to a point interaction for the discrete Schr\"odinger operator. Our goal is to find explicit expressions for the spectral measure, the resolvent and other spectral characteristics of such Jacobi matrices. It turns out that their spectral analysis leads to a new class of orthogonal polynomials generalizing the classical Chebyshev polynomials.

Dates et versions

hal-01503196 , version 1 (06-04-2017)

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Dimitri R Yafaev. A point interaction for the discrete Schr\"odinger operator and generalized Chebyshev polynomials. Journal of Mathematical Physics, 2017, 58 (6), ⟨10.1063/1.4986414⟩. ⟨hal-01503196⟩
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