Non-autonomous multidimensional Toda system and multiple interpolation problem

Abstract

We study the interpolation analogue of the Hermite-Padé type I approximation problem. We provide its determinant solution and we write down the corresponding integrable discrete system as an admissible reduction of Hirota's discrete Kadomtsev-Petviashvili equations. Apart from the $\tau$-function form of the system we provide its variant, which in the simplest case of dimension two reduces to the non-autonomous discrete-time Toda equations.

13 pages; v2 introduction expanded and references added

References in corpus (2)

• The affine Weyl group symmetry of Desargues maps and of the non-commutative Hirota-Miwa system
• Non-commutative Hermite--Padé approximation and integrability

Cited by in corpus (1)

• Determinantal approach to multiple orthogonal polynomials, and the corresponding integrable equations