NONCOMMUTATIVE BISPECTRAL DARBOUX TRANSFORMATIONS

作者：Geiger Joel^*; Horozov Emil; Yakimov Milen

来源：Transactions of the American Mathematical Society, 2017, 369(8): 5889-5919.

DOI：10.1090/tran/6950

• The noncommutative bispectral problem
• Darboux transformations
• matrix rank one bispectral functions
• the Airy bispectral function

We prove a general theorem establishing the bispectrality of noncommutative Darboux transformations. It has a wide range of applications that establish bispectrality of such transformations for differential, difference and q-difference operators with values in all noncommutative algebras. All known bispectral Darboux transformations are special cases of the theorem. Using the methods of quasideterminants and the spectral theory of matrix polynomials, we explicitly classify the set of bispectral Darboux transformations from rank one differential operators and Airy operators with values in matrix algebras. These sets generalize the classical Calogero-Moser spaces and Wilson's adelic Grassmannian.

• 出版日期2017-8
• 单位MIT