Bispectral Darboux transformations: The generalized Airy case
نویسندگان
چکیده
منابع مشابه
Bispectral Darboux Transformations: The Generalized Airy Case
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 s...
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We construct families of bispectral difference operators of the form a(n)T + b(n) + c(n)T 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 Grünbaum, Haine, Horozov, and Iliev they exhaust all bispectral regular (i.e. a(n) 6= 0, c(n) 6= 0,∀n ∈ Z) ...
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For operators of many different kinds it has been proved that (generalized) Darboux transformations can be built using so called Wronskian formulae. Such Darboux transformations are not invertible in the sense that the corresponding mappings of the operator kernels are not invertible. The only known invertible ones were Laplace transformations (and their compositions), which are special cases o...
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ژورنال
عنوان ژورنال: Physica D: Nonlinear Phenomena
سال: 1997
ISSN: 0167-2789
DOI: 10.1016/s0167-2789(96)00208-4