Orthogonal rational functions with real poles, root asymptotics, and GMP matrices

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dc.citation.firstpage1
dc.citation.journalTitleTransactions of the American Mathematical Society, Series B
dc.citation.lastpage47
dc.citation.volumeNumber10
dc.contributor.authorEichinger, Benjamin
dc.contributor.authorLukić, Milivoje
dc.contributor.authorYoung, Giorgio
dc.date.accessioned2023-03-10T19:04:10Z
dc.date.available2023-03-10T19:04:10Z
dc.date.issued2023
dc.description.abstractThere is a vast theory of the asymptotic behavior of orthogonal polynomials with respect to a measure on and its applications to Jacobi matrices. That theory has an obvious affine invariance and a very special role for . We extend aspects of this theory in the setting of rational functions with poles on, obtaining a formulation which allows multiple poles and proving an invariance with respect to preserving Möbius transformations. We obtain a characterization of Stahl–Totik regularity of a GMP matrix in terms of its matrix elements; as an application, we give a proof of a conjecture of Simon – a Cesàro–Nevai property of regular Jacobi matrices on finite gap sets.
dc.identifier.citationEichinger, Benjamin, Lukić, Milivoje and Young, Giorgio. "Orthogonal rational functions with real poles, root asymptotics, and GMP matrices." <i>Transactions of the American Mathematical Society, Series B,</i> 10, (2023) American Mathematical Society: 1-47. https://doi.org/10.1090/btran/117.
dc.identifier.digitalS2330-0000-2023-00117-0
dc.identifier.doihttps://doi.org/10.1090/btran/117
dc.identifier.urihttps://hdl.handle.net/1911/114496
dc.language.isoeng
dc.publisherAmerican Mathematical Society
dc.rightsCopyright 2023 by the author(s) under Creative Commons Attribution-NonCommercial 3.0 License (CC BY NC 3.0)
dc.rights.urihttps://creativecommons.org/licenses/by-nc/3.0/
dc.titleOrthogonal rational functions with real poles, root asymptotics, and GMP matrices
dc.typeJournal article
dc.type.dcmiText
dc.type.publicationpublisher version
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