{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T18:16:57Z","timestamp":1776795417525,"version":"3.51.2"},"reference-count":16,"publisher":"American Mathematical Society (AMS)","issue":"280","license":[{"start":{"date-parts":[[2013,4,2]],"date-time":"2013-04-02T00:00:00Z","timestamp":1364860800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We study polynomials which satisfy the same recurrence relation as the Szeg\u0151 polynomials, however, with the restriction that the (reflection) coefficients in the recurrence are larger than one in modulus. Para-orthogonal polynomials that follow from these Szeg\u0151 polynomials are also considered. With positive values for the reflection coefficients, zeros of the Szeg\u0151 polynomials, para-orthogonal polynomials and associated quadrature rules are also studied. Finally, again with positive values for the reflection coefficients, interlacing properties of the Szeg\u0151 polynomials and polynomials arising from canonical spectral transformations are obtained.<\/p>","DOI":"10.1090\/s0025-5718-2012-02593-2","type":"journal-article","created":{"date-parts":[[2012,4,2]],"date-time":"2012-04-02T13:22:11Z","timestamp":1333372931000},"page":"2229-2249","source":"Crossref","is-referenced-by-count":0,"title":["Szeg\u0151 and para-orthogonal polynomials on the real line: Zeros and canonical spectral transformations"],"prefix":"10.1090","volume":"81","author":[{"given":"Kenier","family":"Castillo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Regina","family":"Lambl\u00e9m","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fernando","family":"Rafaeli","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alagacone","family":"Ranga","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2012,4,2]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1016\/0377-0427(94)00125-1","article-title":"The symmetric strong moment problem","volume":"67","author":"Common, A. 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Fract., 7 (1999), 9\u201322."},{"issue":"4","key":"10","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1007\/s00009-005-0057-3","article-title":"Christoffel transforms and Hermitian linear functionals","volume":"2","author":"Marcell\u00e1n, Francisco","year":"2005","journal-title":"Mediterr. J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/1660-5446","issn-type":"print"},{"issue":"2","key":"11","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1016\/j.cam.2007.06.017","article-title":"Geronimus spectral transforms and measures on the complex plane","volume":"219","author":"Marcell\u00e1n, F.","year":"2008","journal-title":"J. Comput. Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0377-0427","issn-type":"print"},{"key":"12","unstructured":"F.R. 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