dorsal/arxiv
View SchemaBispectral Darboux Transformations: The Generalized Airy Case
| Authors | Alex Kasman, Mitchell Rothstein |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9606018 |
| URL | https://arxiv.org/abs/q-alg/9606018 |
| DOI | 10.1016/S0167-2789(96)00208-4 |
Abstract
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 $r>1$. As a result, the bispectrality of a large family of algebras of rank $r$ 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.
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"abstract": "This paper considers Darboux transformations of a bispectral operator which\npreserve its bispectrality. A sufficient condition for this to occur is given,\nand applied to the case of generalized Airy operators of arbitrary order $r\u003e1$.\nAs a result, the bispectrality of a large family of algebras of rank $r$ is\ndemonstrated. An involution on these algebras is exhibited which exchanges the\nrole of spatial and spectral parameters, generalizing Wilson\u0027s rank one\nbispectral involution. Spectral geometry and the relationship to the Sato\ngrassmannian are discussed.",
"arxiv_id": "q-alg/9606018",
"authors": [
"Alex Kasman",
"Mitchell Rothstein"
],
"categories": [
"q-alg",
"math.QA",
"nlin.SI",
"solv-int"
],
"doi": "10.1016/S0167-2789(96)00208-4",
"title": "Bispectral Darboux Transformations: The Generalized Airy Case",
"url": "https://arxiv.org/abs/q-alg/9606018"
},
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