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- Publisher
- Springer Journals
- Copyright
- Copyright © 2018 by SpringerNature
- Subject
- Mathematics; Mathematics, general; Applications of Mathematics; Computational Mathematics and Numerical Analysis
- eISSN
- 2197-9847
- DOI
- 10.1007/s40687-018-0165-x
- Publisher site
- See Article on Publisher Site
Abstract
We find a new formula for the orthonormal polynomials corresponding to a measure $$\mu $$ μ on the unit circle whose Verblunsky coefficients are periodic. The formula is presented using the Chebyshev polynomials of the second kind and the discriminant of the periodic sequence. We present several applications including a resolution of a problem suggested by Simon (Commun Pure Appl Math 59(7):1042–1062, 2006) regarding the existence of singular points in the bands of the support of the measure and a universality result at all points of the essential support of $$\mu $$ μ .
Journal
Research in the Mathematical Sciences – Springer Journals
Published: Oct 19, 2018