Para-orthogonal polynomials from constant Verblunsky coefficients

M.S. Costa; R.L. Lamblém; J.H. McCabe; A. Sri Ranga

doi:10.1016/j.jmaa.2015.02.005

Para-orthogonal polynomials from constant Verblunsky coefficients

M.S. Costa, R.L. Lamblém, J.H. McCabe, A. Sri Ranga

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Orthogonal polynomials on the unit circle associated with constant Verblunsky coefficients are also known as Geronimus polynomials. We consider the properties of some special sequences of para-orthogonal polynomials that follow from the Geronimus polynomials and, as applications, obtain information concerning certain associated quadrature rules and also other related orthogonal polynomials. Positive chain sequences play an important role in our study.

Original language	English
Pages (from-to)	1040-1060
Journal	Journal of Mathematical Analysis and Applications
Volume	426
Issue number	2
Early online date	4 Feb 2015
DOIs	https://doi.org/10.1016/j.jmaa.2015.02.005
Publication status	Published - 15 Jun 2015

Keywords

Orthogonal polynomials on the unit circle
Constant Verblunsky coefficients
Para-orthogonal polynomials
Positive chain sequences

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10.1016/j.jmaa.2015.02.005

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title = "Para-orthogonal polynomials from constant Verblunsky coefficients",

abstract = "Orthogonal polynomials on the unit circle associated with constant Verblunsky coefficients are also known as Geronimus polynomials. We consider the properties of some special sequences of para-orthogonal polynomials that follow from the Geronimus polynomials and, as applications, obtain information concerning certain associated quadrature rules and also other related orthogonal polynomials. Positive chain sequences play an important role in our study.",

keywords = "Orthogonal polynomials on the unit circle, Constant Verblunsky coefficients, Para-orthogonal polynomials, Positive chain sequences",

author = "M.S. Costa and R.L. Lambl{\'e}m and J.H. McCabe and {Sri Ranga}, A.",

year = "2015",

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T1 - Para-orthogonal polynomials from constant Verblunsky coefficients

AU - Costa, M.S.

AU - Lamblém, R.L.

AU - McCabe, J.H.

AU - Sri Ranga, A.

PY - 2015/6/15

Y1 - 2015/6/15

N2 - Orthogonal polynomials on the unit circle associated with constant Verblunsky coefficients are also known as Geronimus polynomials. We consider the properties of some special sequences of para-orthogonal polynomials that follow from the Geronimus polynomials and, as applications, obtain information concerning certain associated quadrature rules and also other related orthogonal polynomials. Positive chain sequences play an important role in our study.

AB - Orthogonal polynomials on the unit circle associated with constant Verblunsky coefficients are also known as Geronimus polynomials. We consider the properties of some special sequences of para-orthogonal polynomials that follow from the Geronimus polynomials and, as applications, obtain information concerning certain associated quadrature rules and also other related orthogonal polynomials. Positive chain sequences play an important role in our study.

KW - Orthogonal polynomials on the unit circle

KW - Constant Verblunsky coefficients

KW - Para-orthogonal polynomials

KW - Positive chain sequences

U2 - 10.1016/j.jmaa.2015.02.005

DO - 10.1016/j.jmaa.2015.02.005

M3 - Article

SN - 0022-247X

VL - 426

SP - 1040

EP - 1060

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Para-orthogonal polynomials from constant Verblunsky coefficients

Abstract

Keywords

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