Orthogonal polynomials on the unit circle

By Barry Simon. 2004

353 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/73666199aca099fa8ded4218e55983655b6778df

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In Applied Mathematics

Citations in the corpus

The Analytic Theory of Matrix Orthogonal Polynomials (2007, methodology): “s very littleonthesubject inmonographs —the moreclassical ones (e.g., [23, 82, 93, 184]) predate most of the subject; see, however, Atkinson [5, Section 6.6]. Ismail [118] has no discussion and Simon [167, 168] has a single section! Because of the use of MOPRL in [33], we became interested in the su”
Szegö's theorem and its probabilistic descendants (2011, methodology): “§ This involves a sequence of coeﬃcients (not two sequences, as with OPRL), the Verblunsky coeﬃcients α = ( α n ) ( § 2), named (there are several other names in use) and systematically exploited in the magisterial two-volume book on OPUC ([Si4], [Si5]) by Barry Simon.”
Discrete Painlev\'e equations for recurrence coefficients of orthogonal polynomials (2005, neutral): “These were introduced by Hounkonnou et al. in [10].”
CMV matrices: Five years after (2006, background): “…(Section 11) (7) an argument of AGR is made explicit and streamlined to go from AGR to LM factorization (Section 10) It is a pleasure to thank M. Cantero, P. Deift, L. Golinskii, F. Marcellán, A. Mart́inez-Finkelshtein, L. Moral, I. Nenciu, P. Nevai, L. Velázquez, and D. Watkins for useful input.”
EQUILIBRIUM MEASURES AND CAPACITIES IN SPECTRAL THEORY (2007, background): “Here one issue will be that if E = ∂D, the zero density may not converge to a measure on ∂D.”
Asymptotics of Toeplitz, Hankel, and Toeplitz+Hankel determinants with Fisher-Hartwig singularities (2009, methodology): “nd Hankel determinants. Here we present aspects of the theory of orthogonal polynomials on the unit circle we use in this work. Some of the properties we describe here are well-known (see, e.g. [38], [37]), the others not so. We also adapt the theory to complex weights we need in this work, while in”
Two extensions of Lubinsky’s universality theorem (2008, background): “(a) Instead of requiring σ(dµ) = [−1, 1], we want to allow σ ess (dµ) = [−1, 1], as is natural if one makes assumptions on {a n , b n } ∞ n=1 rather than directly on dµ.”
Jost functions and Jost solutions for Jacobi matrices, I. A necessary and sufficient condition for Szegő asymptotics (2005, background): “Unfortunately, there are some errors in the analogous formula in [44], namely, (13.”
FINE STRUCTURE OF THE ZEROS OF ORTHOGONAL POLYNOMIALS, I. A TALE OF TWO PICTURES (2004, background): “[8] D. Damanik and B. Simon, Jost functions and Jost solutions for Jacobi matrices, II.”
Orthogonal polynomials on the unit circle: New results (2004, result): “Totik's Workshop.”