The spectral matrices of Toda solitons and the fundamental solution of some discrete heat equations
Annales de l'Institut Fourier, Volume 55 (2005) no. 6, pp. 1765-1788.

The Stieltjes spectral matrix measure of the doubly infinite Jacobi matrix associated with a Toda g-soliton is computed, using Sato theory. The result is used to give an explicit expansion of the fundamental solution of some discrete heat equations, in a series of Jackson’s q-Bessel functions. For Askey-Wilson type solitons, this expansion reduces to a finite sum.

A l’aide de la théorie de Sato, on calcule la matrice spectrale de Stieltjes associée à une matrice de Jacobi doublement infinie, donnant lieu à une solution g-soliton du réseau de Toda. On utilise ce résultat pour donner un développement explicite de la solution fondamentale de versions discrètes de l’équation de la chaleur, en termes d’une série des q-déformations de Jackson des fonctions de Bessel. Pour les solitons dits de Askey-Wilson, ce développement se réduit à une somme finie.

DOI: 10.5802/aif.2140
Classification: 35Q51, 37K20, 39A13
Keywords: Heat kernel, Toda lattice hierarchy
Mot clés : noyau de la chaleur, réseau de Toda
Haine, Luc 1

1 Université catholique de Louvain, institut de mathématique pure et appliquée, chemin du Cyclotron 2, 1348 Louvain-la-Neuve (Belgique)
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Haine, Luc. The spectral matrices of Toda solitons and the fundamental solution of some discrete heat equations. Annales de l'Institut Fourier, Volume 55 (2005) no. 6, pp. 1765-1788. doi : 10.5802/aif.2140. http://archive.numdam.org/articles/10.5802/aif.2140/

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