Taiwanese Journal of Mathematics

Non-classical Orthogonality Relations for Continuous q-Jacobi Polynomials

Samuel G. Moreno and Esther M. García-Caballero

Full-text: Open access

Abstract

We consider the continuous $q$-Jacobi polynomials $\{P_n^{(\alpha,\beta)}(\cdot|q)\}_{n=0}^{\infty}$, extending the variable and the parameters beyond classical considerations. For those new allowed values of the parameters for which Favard's theorem fails to work, we construct inner products in which the presence of the Askey-Wilson divided difference operator provides the $q$-Sobolev character of the non-standard orthogonality for the corresponding family.

Article information

Source
Taiwanese J. Math., Volume 15, Number 4 (2011), 1677-1690.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406372

Digital Object Identifier
doi:10.11650/twjm/1500406372

Mathematical Reviews number (MathSciNet)
MR2848982

Zentralblatt MATH identifier
1237.33010

Subjects
Primary: 33D45: Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) 42C05: Orthogonal functions and polynomials, general theory [See also 33C45, 33C50, 33D45]

Keywords
continuous $q$-Jacobi polynomials non-standard orthogonality Favard's theorem

Citation

Moreno, Samuel G.; García-Caballero, Esther M. Non-classical Orthogonality Relations for Continuous q-Jacobi Polynomials. Taiwanese J. Math. 15 (2011), no. 4, 1677--1690. doi:10.11650/twjm/1500406372. https://projecteuclid.org/euclid.twjm/1500406372


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References

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