Higher-order Szegő theorems with two singular points
نویسندگان
چکیده
منابع مشابه
Higher-order Szego theorems with two singular points
We consider probability measures, dμ = w(θ) dθ 2π+dμs, on the unit circle, ∂D, with Verblunsky coefficients, {αj}j=0. We prove for θ1 6= θ2 in [0, 2π) that ∫ [1− cos(θ − θ1)][1− cos(θ − θ2)] logw(θ) dθ 2π > −∞ if and only if ∞ ∑ j=0 ∣∣{(δ − e−iθ2)(δ − e−iθ1)α} j ∣∣2 + |αj | <∞ where δ is the left shift operator (δβ)j = βj+1. We also prove that ∫ (1− cos θ) logw(θ) dθ 2π > −∞
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2005
ISSN: 0021-9045
DOI: 10.1016/j.jat.2005.02.003