Bispectral Darboux Transformations: The Generalized Airy Case
q-alg
2009-10-30 v1 量子代数
可精确求解与可积系统
solv-int
摘要
This paper considers Darboux transformations of a bispectral operator which preserve its bispectrality. A sufficient condition for this to occur is given, and applied to the case of generalized Airy operators of arbitrary order . As a result, the bispectrality of a large family of algebras of rank is demonstrated. An involution on these algebras is exhibited which exchanges the role of spatial and spectral parameters, generalizing Wilson's rank one bispectral involution. Spectral geometry and the relationship to the Sato grassmannian are discussed.
关键词
引用
@article{arxiv.q-alg/9606018,
title = {Bispectral Darboux Transformations: The Generalized Airy Case},
author = {Alex Kasman and Mitchell Rothstein},
journal= {arXiv preprint arXiv:q-alg/9606018},
year = {2009}
}
备注
LaTeX, to appear in Physica D, a nicer postscript version is available at http://www.math.uga.edu/~kasman/