Matrix valued bispectral operators and quasideterminants

BOYALLIAN, CARINA; LIBERATI, JOSE I.

JOURNAL OF PHYSICS. A - MATHEMATICAL AND GENERAL

IOP publishing

Año: 2008 vol. 41 p. 1 - 11

0305-4470

We consider a matrix-valued version of the bispectral problem, that is, find differential operators and with matrix coefficients such that there exists a family of matrix-valued common eigenfunctions ψ(x, z): where f and Θ are matrix-valued functions. Using quasideterminants, we prove that the operators L obtained by non-degenerated rational matrix Darboux transformations from are bispectral operators, where and D is a diagonal matrix. We also give a procedure to find an explicit formula for the operator B extending previous results in the scalar case.