Generalized trace formula and asymptotics of the averaged Turan determinant for polynomials orthogonal with a discrete Sobolev inner product
نویسنده
چکیده
Let be a finite positive Borel measure supported on [−1, 1] and introduce the discrete Sobolev-type inner product 〈f, g〉 = ∫ 1 −1 f (x)g(x) d (x)+ K ∑ k=1 Nk ∑ i=0 Mk,if (ak)g (ak), where the mass points ak belong to [−1, 1], and Mk,i > 0(i = 0, 1, . . . , Nk). In this paper, we obtain generalized trace formula and asymptotics of the averagedTuran determinant for the Sobolev-type orthogonal polynomials. Asymptotics of the recurrence coefficients for symmetric Gegenbauer–Sobolev orthogonal polynomials is obtained. Trace formula and asymptotics of Turan’s determinant for Gegenbauer–Sobolev orthogonal polynomials are also given. © 2006 Elsevier Inc. All rights reserved.
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ورودعنوان ژورنال:
- Journal of Approximation Theory
دوره 141 شماره
صفحات -
تاریخ انتشار 2006