The spectral matrices of Toda solitons and the fundamental solution of some discrete heat equations

Luc Haine[1]

  • [1] Université catholique de Louvain, institut de mathématique pure et appliquée, chemin du Cyclotron 2, 1348 Louvain-la-Neuve (Belgique)

Annales de l’institut Fourier (2005)

  • Volume: 55, Issue: 6, page 1765-1788
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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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 55.6 (2005): 1765-1788. <http://eudml.org/doc/116232>.

@article{Haine2005,
abstract = {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.},
affiliation = {Université catholique de Louvain, institut de mathématique pure et appliquée, chemin du Cyclotron 2, 1348 Louvain-la-Neuve (Belgique)},
author = {Haine, Luc},
journal = {Annales de l’institut Fourier},
keywords = {Heat kernel; Toda lattice hierarchy; heat kernel; discrete heat equations; Jackson’s -Bessel functions},
language = {eng},
number = {6},
pages = {1765-1788},
publisher = {Association des Annales de l'Institut Fourier},
title = {The spectral matrices of Toda solitons and the fundamental solution of some discrete heat equations},
url = {http://eudml.org/doc/116232},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Haine, Luc
TI - The spectral matrices of Toda solitons and the fundamental solution of some discrete heat equations
JO - Annales de l’institut Fourier
PY - 2005
PB - Association des Annales de l'Institut Fourier
VL - 55
IS - 6
SP - 1765
EP - 1788
AB - 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.
LA - eng
KW - Heat kernel; Toda lattice hierarchy; heat kernel; discrete heat equations; Jackson’s -Bessel functions
UR - http://eudml.org/doc/116232
ER -

References

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