Orthogonal Polynomial Interpretation of q-Toda and q-Volterra Equations

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...

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Bibliographic Details
Published in:Bulletin of the Malaysian Mathematical Sciences Society 2018, Vol.41 (1), p.393-414
Main Authors: Area, I., Branquinho, A., Moreno, A. Foulquié, Godoy, E.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators
Polynomials
Volterra integral equations
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Summary: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 D q . 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.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-016-0305-7