OPUC on one foot

By Barry Simon. 2005

97 citations recorded by the source corpus.

We present an expository introduction to orthogonal polynomials on the unit circle.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c57095932f49a30a4878e080de6abc1f5f0bfd5d

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In Applied Mathematics

In Computational Theory and Mathematics

In Statistics and Probability

Citations in the corpus

Szegö's theorem and its probabilistic descendants (2011, background): “OPUC) dates back to Szeg¨o’s work of 1915-21, and has been given a great impetus by the recent work of Simon, in particular his two-volume book [Si4], [Si5], the survey paper (or summary of the book) [Si3], and the book [Si9], whose title we allude to in ours. Simon’s motivation comes from spectral ”
Rank one perturbations and the zeros of paraorthogonal polynomials on the unit circle (2006, background): “ar X iv :m at h/ 06 06 03 7v 1 [ m at h. SP ] 1 J un 2 00 6 R A N K O N E PERT U R B AT IO N S A N D T H E ZER O S O F PA R A O RT H O G O N A L PO LY N O M IA LS O N T H E U N IT C IR C LE BARRY SIM O N* A bstract.”
Hodge Laplacians on graphs (2015, background): “The occasional whimsical section headings are inspired by [11, 50, 51, 59, 60].”
The Christoffel-Darboux Kernel (2008, methodology): “se, {αn}∞ n=0 determine dµ, while in the OPRL case, they do if sup(|an| + |bn|) < ∞, and may or may not in the unbounded case. For basics of OPRL, see [93, 22, 34, 89]; and for basics of OPUC, see [93, 37, 34, 80, 81, 79]. We will use κn (or κn(dµ)) for the leading coeﬃcient of xn, pn, or ϕn, so ”
CMV matrices: Five years after (2006, background): “While Verblunsky [81] defined the n in a different (albeit equivalent) way, he proved a theorem (called Verblusnky’s theorem in [69]; see also [68]) that says this map d → { n}∞n=0 is one–one and onto all of D∞, so (1)–(3) for the unitary case have been well understood for 65 years.”