van Diejen, J. F. A Sato formula for reflectionless finite difference operators. (English) Zbl 0997.37054 J. Math. Phys. 40, No. 11, 5822-5834 (1999). This paper aims at exhibiting an analogous Sato formula for the eigenfunctions of the reflectionless Jacobi operators. To this end the author employs inverse-scattering techniques for these operators that have their origin in the celebrated work of Flaschka on the soliton dynamics of the infinite Toda chain. Reviewer: Messoud Efendiev (Berlin) Cited in 1 Document MSC: 37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems 39A70 Difference operators 47B36 Jacobi (tridiagonal) operators (matrices) and generalizations Keywords:Sato formula; eigenfunctions; reflectionless Jacobi operators; inverse-scattering; infinite Toda chain PDFBibTeX XMLCite \textit{J. F. van Diejen}, J. Math. Phys. 40, No. 11, 5822--5834 (1999; Zbl 0997.37054) Full Text: DOI References: [1] Sato M., RIMS KôkyûRoku 439 pp 30– (1981) [2] DOI: 10.2977/prims/1195182017 · Zbl 0557.35091 · doi:10.2977/prims/1195182017 [3] DOI: 10.1007/BF02698802 · Zbl 0592.35112 · doi:10.1007/BF02698802 [4] DOI: 10.1143/PTPS.94.210 · doi:10.1143/PTPS.94.210 [5] DOI: 10.1143/PTP.51.703 · Zbl 0942.37505 · doi:10.1143/PTP.51.703 [6] DOI: 10.1016/0370-1573(75)90018-6 · doi:10.1016/0370-1573(75)90018-6 [7] DOI: 10.1007/s002200050419 · Zbl 0914.39018 · doi:10.1007/s002200050419 [8] DOI: 10.1007/PL00004732 · Zbl 0935.37045 · doi:10.1007/PL00004732 [9] DOI: 10.1143/JPSJ.35.286 · doi:10.1143/JPSJ.35.286 [10] DOI: 10.1090/S0002-9947-1993-1153014-1 · doi:10.1090/S0002-9947-1993-1153014-1 [11] DOI: 10.1063/1.1666237 · doi:10.1063/1.1666237 [12] DOI: 10.1063/1.1666610 · doi:10.1063/1.1666610 [13] DOI: 10.1016/0001-8708(75)90148-6 · Zbl 0306.34001 · doi:10.1016/0001-8708(75)90148-6 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.