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Title of Journal: Constr Approx

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Abbravation: Constructive Approximation

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Springer-Verlag

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10.1016/0022-2828(90)90963-3

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1432-0940

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The Genetic Sums Representation for the Moments o

Authors: A Aptekarev V Kaliaguine J Van Iseghem
Publish Date: 2000/01/01
Volume: 16, Issue: 4, Pages: 487-524
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Abstract

This paper deals with the spectral problems for highorder nonsymmetric difference operators The method of investigation is based on the analysis of the genetic sums formulas for the moments of the operator The parameters of these sums are shown to be connected with coefficients of the introduced vector Stieltjes continued fraction The connections with vector orthogonality Hermite—Padé approximation and Hankel determinants are investigated This gives a tool for the analysis of the solution of the direct and inverse spectral problem of the operator It is applied to the integration of hierarchy of the discrete KdV equations The existence of a global solution is proved


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