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Title: Orthogonal polynomial interpretation of q-Toda and q-Volterra equations
Author: Área, Ivan
Branquinho, Amílcar
Godoy, Eduardo
Moreno, Ana Foulquié
Keywords: q-Difference equations
Recurrence relations
Orthogonal polynomials
q-Toda equations
q-Volterra equations
Lax type theorems
Issue Date: Jan-2018
Publisher: Springer Singapore
Abstract: The correspondences between dynamics of q-Toda and q-Volterra equations for the coefficients of the Jacobi operator and its resolvent function are established. The orthogonal polynomials associated with these Jacobi operators satisfy an Appell condition, with respect to the q-difference operator Dq . Lax type theorems for the point spectrum of the Jacobi operators associated with these equations are obtained. Examples related with the big q-Legendre, discrete q-Hermite I, and little q-Laguerre orthogonal polynomials and q-Toda and q-Volterra equations are given.
Peer review: yes
DOI: 10.1007/s40840-016-0305-7
ISSN: 0126-6705
Appears in Collections:CIDMA - Artigos
CHAG - Artigos

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