Abstract
In this paper, we consider a general Sobolev inner product on the unit circle of the follwing type: 〈f(z),g(z)〉 s= ∑ j=0 p ∫ 0 2π f (j) e iθ g (j)(e iθ) dμ j(θ), z=e iθ , with μj ( j = 0, …, p) finite positive Borel measures on [0, 2π] and p a positive integer p ⪰ 1. Under the assumption that the Caratheodory functions of measures μ 0,…, μ p −1 and the Szegő function of measure μ p have analytic extension outside the open unit disk, we prove that Szegő's asymptotic formula holds true for the Sobolev orthogonal polynomials.
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