Strong Asymptotic Behavior and Weak Convergence of Polynomials Orthogonal on an Arc of the Unit Circle
نویسندگان
چکیده
منابع مشابه
Perturbation of Orthogonal Polynomials on an Arc of the Unit Circle
Orthogonal polynomials on the unit circle are completely determined by their reflection coefficients through the Szegő recurrences. We assume that the reflection coefficients converge to some complex number a with 0 < |a| < 1. The polynomials then live essentially on the arc { e : α ≤ θ ≤ 2π−α } where cos α 2 def = √ 1− |a|2 with α ∈ (0, π). We analyze the orthogonal polynomials by comparing th...
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We show that ratio asymptotics of orthogonal polynomials on the circle imply ratio asymptotics for all their derivatives. Moreover, by reworking ideas of P. Nevai, we show that uniform asymptotics for orthogonal polynomials on an arc of the unit circle imply asymptotics for all their derivatives. Let be a nite positive Borel measure on the unit circle (or [0; 2 ]). Let f'ng denote the orthonor...
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Even though the theory of orthogonal polynomials on the unit circle, also known as the theory of Szegő polynomials, is very extensive, it is less known than the theory of orthogonal polynomials on the real line. One reason for this may be that “beautiful” examples on the theory of Szegő polynomials are scarce. This is in contrast to the wonderful examples of Jacobi, Laguerrer and Hermite polyno...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2001
ISSN: 0021-9045
DOI: 10.1006/jath.2001.3574