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- W2046848113 abstract "In this paper, we provide a solution of the quadrature sum problem of R. Askey for a class of Freud weights. Let r > 0, b ∈ (− ∞, 2]. We establish a full quadrature sum estimate ∑ j=1 n λ jn |PW| p (x jn )W −b ↬C ∫ −∞ ∞ |PW| p (t)W 2−b (t) d t 1 ⩽ p < ∞, for every polynomial P of degree at most n + rn 1 3 , where W 2 is a Freud weight such as exp (−¦x¦ α ) , α > 1, λ jn are the Christoffel numbers, x jn are the zeros of the orthonormal polynomials for the weight W 2 , and C is independent of n and P . We also prove a generalisation, and that such an estimate is not possible for polynomials P of degree ⩽ m = m ( n ) if m(n) = n + ξ n n 1 3 , where ξ n → ∞ as n → ∞. Previous estimates could sum only over those x jn with ¦x jn ¦ ⩽ σx 1n , some fixed 0 < σ < 1." @default.
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- W2046848113 date "1995-06-01" @default.
- W2046848113 modified "2023-09-29" @default.
- W2046848113 title "Full quadrature sums for pth powers of polynomials with Freud weights" @default.
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- W2046848113 doi "https://doi.org/10.1016/0377-0427(94)00045-3" @default.
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