2024-03-29T14:34:26Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/790652022-11-17T02:08:08Zhdl_2115_20039hdl_2115_116Simple matrix representations of the orthogonal polynomials for a rational spectral density on the unit circleInoue, AkihikoKasahara, YukioOrthogonal polynomials on the unit circleVerblunsky coefficientsRational spectral densitySeghier's formula410In this note, by using a discrete analog of a projection formula introduced by A. Seghier in 1978, we calculate the orthogonal polynomials on the unit circle for a rational spectral density having no zeros there, and derive simple matrix representations of themselves, their squared norms, and the Verblunsky coefficients. (C) 2018 Elsevier Inc. All rights reserved.ElsevierJournal Articleapplication/pdfhttp://hdl.handle.net/2115/79065https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/79065/1/IK-JMAA-rev.pdf0022-247XJournal of mathematical analysis and applications4642136613742018-08-15enginfo:doi/10.1016/j.jmaa.2018.04.062©2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/author