66 citations · 603 across the 77 of their papers we have counts for
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Automorphisms of the Weyl algebra and bispectral operators
B. Bakalov, E. Horozov, M. Yakimov
In our previous paper q-alg/9605011 we proposed several algebraic methods for constructing new solutions to the bispectral problem. In the present note the corresponding eigenfunct…
General methods for constructing bispectral operators
B. Bakalov, E. Horozov, M. Yakimov
We present methods for obtaining new solutions to the bispectral problem. We achieve this by giving its abstract algebraic version suitable for generalizations. All methods are ill…
Highest weight modules over W_{1+infty} algebra and the bispectral problem
B. Bakalov, E. Horozov, M. Yakimov
The present paper establishes a connection between the Lie algebra W_{1+infty} and the bispectral problem. We show that the manifolds of bispectral operators obtained by Darboux tr…
Bäcklund--Darboux transformations in Sato's Grassmannian
B. Bakalov, E. Horozov, M. Yakimov
We define Bäcklund--Darboux transformations in Sato's Grassmannian. They can be regarded as Darboux transformations on maximal algebras of commuting ordinary differential operators…
Highest weight modules of W_{1+infty}, Darboux transformations and the bispectral problem
B. Bakalov, E. Horozov, M. Yakimov
We announce a systematic way for constructing bispectral algebras of commuting differential operators of any rank N. It enables us to obtain all previously known classes and exampl…
Bispectral algebras of commuting ordinary differential operators
B. Bakalov, E. Horozov, M. Yakimov
We develop a systematic way for constructing bispectral algebras of commuting ordinary differential operators of any rank . It combines and unifies the ideas of Duistermaat-Grün…