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- W2257022383 abstract "We introduce the Szego class, Sz(E), for an arbitrary Parreau-Widom set E in R and study the dynamics of its elements under the left shift. When the direct Cauchy theorem holds on CE, we show that to each J in Sz(E) there is a unique element J' in the isospectral torus, T_E, so that the left-shifts of J are asymptotic to the orbit {J'_m} on T_E. Moreover, we show that the ratio of the associated orthogonal polynomials has a limit, expressible in terms of Jost functions, as the degree n tends to infinity. This enables us to describe the large n behaviour of the orthogonal polynomials for every J in the Szego class." @default.
- W2257022383 created "2016-06-24" @default.
- W2257022383 creator A5007401767 @default.
- W2257022383 date "2016-02-12" @default.
- W2257022383 modified "2023-09-27" @default.
- W2257022383 title "Dynamics in the Szego class and polynomial asymptotics" @default.
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