Szegő recurrence for multiple orthogonal polynomials on the unit circle
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- by Rostyslav Kozhan and Marcus Vaktnäs;
- Proc. Amer. Math. Soc. 152 (2024), 2983-2997
- DOI: https://doi.org/10.1090/proc/16811
- Published electronically: May 22, 2024
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Abstract:
We investigate polynomials that satisfy simultaneous orthogonality conditions with respect to several measures on the unit circle. We generalize the direct and inverse Szegő recurrence relations, identify the analogues of the Verblunsky coefficients, and prove the Christoffel–Darboux formula. These results should be viewed as the direct analogue of the nearest neighbour recurrence relations from the theory of multiple orthogonal polynomials on the real line.References
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Bibliographic Information
- Rostyslav Kozhan
- Affiliation: Department of Mathematics, Uppsala University, S-751 06 Uppsala, Sweden
- MR Author ID: 872481
- Email: rostyslav.kozhan@math.uu.se
- Marcus Vaktnäs
- Affiliation: Department of Mathematics, Uppsala University, S-751 06 Uppsala, Sweden
- ORCID: 0009-0003-6222-5723
- Email: marcus.vaktnas@math.uu.se
- Received by editor(s): September 20, 2023
- Received by editor(s) in revised form: December 17, 2023, and January 15, 2024
- Published electronically: May 22, 2024
- Communicated by: Mourad Ismail
- © Copyright 2024 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 152 (2024), 2983-2997
- MSC (2020): Primary 42C05; Secondary 41A21, 47B36
- DOI: https://doi.org/10.1090/proc/16811
- MathSciNet review: 4753282