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Boyallian, Carina; Liberati, Jose I, E-mail: boyallia@mate.uncor.edu, E-mail: liberati@mate.uncor.edu2008
AbstractAbstract
[en] We consider a matrix-valued version of the bispectral problem, that is, find differential operators L(x,d/dx) and B(z,d/dz) with matrix coefficients such that there exists a family of matrix-valued common eigenfunctions ψ(x, z): L(x,d/dx)ψ(x,z)=f(z)ψ(x,z), ψ(x,z)B(z,d/dz)=Θ(x)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 g(d/dx)D are bispectral operators, where g(y) element of C[y] 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
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Source
S1751-8113(08)80284-3; Available from http://dx.doi.org/10.1088/1751-8113/41/36/365209; Country of input: International Atomic Energy Agency (IAEA)
Record Type
Journal Article
Journal
Journal of Physics. A, Mathematical and Theoretical (Online); ISSN 1751-8121;
; v. 41(36); [11 p.]

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