Discrete bispectral Darboux transformations from Jacobi operators
经典分析与常微分方程
2007-05-23 v1
摘要
We construct families of bispectral difference operators of the form a(n)T + b(n) + c(n) T^{-1} where T is the shift operator. They are obtained as discrete Darboux transformations from appropriate extensions of Jacobi operators. We conjecture that along with operators previously constructed by Grunbaum, Haine, Horozov, and Iliev they exhaust all bispectral regular (i.e. a(n)c(n) \neq 0, for all integer n) operators of the form above.
引用
@article{arxiv.math/0012191,
title = {Discrete bispectral Darboux transformations from Jacobi operators},
author = {F. Alberto Grünbaum and Milen Yakimov},
journal= {arXiv preprint arXiv:math/0012191},
year = {2007}
}
备注
30 pages, AMS latex