scholarly journals CMV Matrices with Super Exponentially Decaying Verblunsky Coefficients

2014 ◽  
Vol 9 (5) ◽  
pp. 282-294
Author(s):  
M. Zinchenko
Keyword(s):  
Verblunsky Coefficients

scholarly journals Generic spectral results for CMV matrices with dynamically defined Verblunsky coefficients

2020 ◽  
Vol 279 (12) ◽  
pp. 108803
Author(s):  
Licheng Fang ◽  
David Damanik ◽  
Shuzheng Guo
Keyword(s):  
Verblunsky Coefficients

scholarly journals Homeomorphisms of S1 and Factorization

2019 ◽  
Author(s):  
Mark Dalthorp ◽  
Doug Pickrell
Keyword(s):  
Fourier Series ◽  
Finite Type ◽  
Parameter Family ◽  
Complex Parameter ◽  
Triangular Factorization ◽  
Linear Fractional Transformations ◽  
Root Subgroup ◽  
Decay Properties ◽  
Group Of Homeomorphisms ◽  
Verblunsky Coefficients

Abstract For each $n>0$ there is a one complex parameter family of homeomorphisms of the circle consisting of linear fractional transformations “conjugated by $z \to z^n$”. We show that these families are free of relations, which determines the structure of “the group of homeomorphisms of finite type”. We next consider factorization for more robust groups of homeomorphisms. We refer to this as root subgroup factorization (because the factors correspond to root subgroups). We are especially interested in how root subgroup factorization is related to triangular factorization (i.e., conformal welding) and correspondences between smoothness properties of the homeomorphisms and decay properties of the root subgroup parameters. This leads to interesting comparisons with Fourier series and the theory of Verblunsky coefficients.

scholarly journals Asymptotic behaviour of Verblunsky coefficients

2006 ◽  
Vol 324 (2) ◽  
pp. 1050-1061
Author(s):  
María Pilar Alfaro ◽  
Manuel Bello Hernández ◽  
Jesús María Montaner
Keyword(s):  
Asymptotic Behaviour ◽  
Verblunsky Coefficients
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