caa a22 4500 475743687 CHVBK 20180406123506.0 cr unu---uuuuu 170329e20001001xx s 000 0 eng 10.1007/s003650010004 doi (NATIONALLICENCE)springer-10.1007/s003650010004 The Genetic Sums' Representation for the Moments of a System of Stieltjes Functions and its Application [Elektronische Daten] [A. Aptekarev, V. Kaliaguine, J. Van Iseghem] Abstract. : This paper deals with the spectral problems for high-order 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. Springer-Verlag New York, 2000 Key words. Genetic sums Stieltjes functions, Nonsymmetric difference operators, Vector orthogonality, Hermite—Padé approximation, Vector continued fraction nationallicence Direct and inverse spectral problem, Discrete KdV equations nationallicence AMS Classification nationallicence 41A20.21 nationallicence 47A10 nationallicence 47B99 nationallicence 30B70 nationallicence Aptekarev A. Keldysh Institute of Applied Mathematics aptekaa@rfbr.ru, Russian Academy of Sciences Miusskaya sq.4 Moscow Russia, RU aut Kaliaguine V. Nizhny Novgorod State Technical University kalia@waise.nntu.sci-nnov.ru, Nizhny Novgorod Minina 24 603600 Russia, RU aut Van Iseghem J. UFR de Mathématiques France jvaniseg.@ano.univ-lille1.fr, Université des Sciences et Technologies de Lille F-59655 Villeneuve d'Ascq Cedex, FR aut https://doi.org/10.1007/s003650010004 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s003650010004 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Aptekarev A. Keldysh Institute of Applied Mathematics aptekaa@rfbr.ru, Russian Academy of Sciences Miusskaya sq.4 Moscow Russia, RU aut NATIONALLICENCE 700 1- Kaliaguine V. Nizhny Novgorod State Technical University kalia@waise.nntu.sci-nnov.ru, Nizhny Novgorod Minina 24 603600 Russia, RU aut NATIONALLICENCE 700 1- Van Iseghem J. UFR de Mathématiques France jvaniseg.@ano.univ-lille1.fr, Université des Sciences et Technologies de Lille F-59655 Villeneuve d'Ascq Cedex, FR aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer