Orthogonality relations for Al-Salam–Carlitz polynomials of type II

Wolter Groenevelt

doi:10.1016/j.jat.2014.07.006

Orthogonality relations for Al-Salam–Carlitz polynomials of type II

Wolter Groenevelt

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Abstract

By use of a special case of Slater’s q-beta integral evaluation formula, we determine orthogonality relations for the Al-Salam–Carlitz polynomials of type II with respect to a family of measures supported on a discrete subset of R. From spectral analysis of the corresponding second-order q-difference operator we obtain an infinite set of functions that complement the Al-Salam–Carlitz II polynomials to an orthogonal basis of the associated L2-space.

Original language	English
Pages (from-to)	89-108
Number of pages	20
Journal	Journal of Approximation Theory
Volume	195
DOIs	https://doi.org/10.1016/j.jat.2014.07.006
Publication status	Published - 2015

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title = "Orthogonality relations for Al-Salam–Carlitz polynomials of type II",

abstract = "By use of a special case of Slater{\textquoteright}s q-beta integral evaluation formula, we determine orthogonality relations for the Al-Salam–Carlitz polynomials of type II with respect to a family of measures supported on a discrete subset of R. From spectral analysis of the corresponding second-order q-difference operator we obtain an infinite set of functions that complement the Al-Salam–Carlitz II polynomials to an orthogonal basis of the associated L2-space.",

author = "Wolter Groenevelt",

year = "2015",

doi = "10.1016/j.jat.2014.07.006",

language = "English",

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journal = "Journal of Approximation Theory",

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T1 - Orthogonality relations for Al-Salam–Carlitz polynomials of type II

AU - Groenevelt, Wolter

PY - 2015

Y1 - 2015

N2 - By use of a special case of Slater’s q-beta integral evaluation formula, we determine orthogonality relations for the Al-Salam–Carlitz polynomials of type II with respect to a family of measures supported on a discrete subset of R. From spectral analysis of the corresponding second-order q-difference operator we obtain an infinite set of functions that complement the Al-Salam–Carlitz II polynomials to an orthogonal basis of the associated L2-space.

AB - By use of a special case of Slater’s q-beta integral evaluation formula, we determine orthogonality relations for the Al-Salam–Carlitz polynomials of type II with respect to a family of measures supported on a discrete subset of R. From spectral analysis of the corresponding second-order q-difference operator we obtain an infinite set of functions that complement the Al-Salam–Carlitz II polynomials to an orthogonal basis of the associated L2-space.

U2 - 10.1016/j.jat.2014.07.006

DO - 10.1016/j.jat.2014.07.006

M3 - Article

SN - 0021-9045

VL - 195

SP - 89

EP - 108

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

ER -

Orthogonality relations for Al-Salam–Carlitz polynomials of type II

Abstract

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