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Keldysh Institute preprints, 2015, 088, 20 pp. (Mi ipmp2050)  

This article is cited in 2 scientific papers (total in 2 papers)

Completely integrable on $\mathbb{Z}_+^d$ potentials for electromagnetic Schrodinger operator: rays asymptotics and scattering problem

A. I. Aptekarev, S. A. Denisov, M. Yattselev


Abstract: The electromagnetic Schrodinger operator in $l_2(\mathbb{Z}_+^d)$ is considered. The potential satisfies to a discrete integrable system related with multiple orthogonal polynomials with respect to the Angelesco system of measures. The problem on limits of the potential along the rays in $\mathbb{Z}_+^d$ is solved. A statement and solution of the scattering problem is considered as well.

Keywords: Difference operator; multiple orthogonal polynomials; discrete integrable systems; scattering problem.

Funding Agency Grant Number
Russian Science Foundation 14-21-00025


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Full text: http:/.../preprint.asp?id=2015-88&lg=r
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UDC: 517.53+517.9

Citation: A. I. Aptekarev, S. A. Denisov, M. Yattselev, “Completely integrable on $\mathbb{Z}_+^d$ potentials for electromagnetic Schrodinger operator: rays asymptotics and scattering problem”, Keldysh Institute preprints, 2015, 088, 20 pp.

Citation in format AMSBIB
\Bibitem{AptDenYat15}
\by A.~I.~Aptekarev, S.~A.~Denisov, M.~Yattselev
\paper Completely integrable on $\mathbb{Z}_+^d$ potentials for electromagnetic Schrodinger operator: rays asymptotics and scattering problem
\jour Keldysh Institute preprints
\yr 2015
\papernumber 088
\totalpages 20
\mathnet{http://mi.mathnet.ru/ipmp2050}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. I. Aptekarev, S. A. Denisov, M. L. Yattselev, “Samosopryazhennye matritsy Yakobi na grafakh i sovmestno ortogonalnye mnogochleny”, Preprinty IPM im. M. V. Keldysha, 2018, 003, 27 pp.  mathnet  crossref  elib
    2. A. I. Aptekarev, R. Kozhan, “Differential equations for the radial limits in $\mathbb{Z}_+^2$ of the solutions of a discrete integrable system”, Preprinty IPM im. M. V. Keldysha, 2018, 214, 20 pp.  mathnet  crossref
  • Препринты Института прикладной математики им. М. В. Келдыша РАН
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