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 inBulletin of the Malaysian Mathematical Sciences Society Vol. 41; no. 1; pp. 393 - 414
Main Authors Area, I., Branquinho, A., Moreno, A. Foulquié, Godoy, E.
Format Journal Article
LanguageEnglish
Published Singapore Springer Singapore 2018
Springer Nature B.V
Subjects
Applications of Mathematics
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators
Polynomials
Volterra integral equations
65Q20
65Q10
33D45
Difference equations
Volterra equations
Orthogonal polynomials
Toda equations
Recurrence relations
Lax type theorems
65Q30
42C05
47N20
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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