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A Sato formula for reflectionless finite difference operators. (English) Zbl 0997.37054

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.

MSC:

37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
39A70 Difference operators
47B36 Jacobi (tridiagonal) operators (matrices) and generalizations
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[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
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