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- W2077377218 abstract "Upper and lower bounds for generalized Christoffel functions, called Freud-Christoffel functions, are obtained. These have the form λn,p(W,j,x) = inf‖PW‖Lp(R)|P(j)(X)| where the infimum is taken over all polynomials P(x) of degree at most n − 1. The upper and lower bounds for λn,p(W,j,x) are obtained for all 0 < p ⩽ ∞ and j = 0, 1, 2, 3,… for weights W(x) = exp(−Q(x)), where, among other things, Q(x) is bounded in [− A, A], and Q″ is continuous in Rβ(−A, A) for some A > 0. For p = ∞, the lower bounds give a simple proof of local and global Markov-Bernstein inequalities. For p = 2, the results remove some restrictions on Q in Freud's work. The weights considered include W(x) = exp(− ¦x¦α2), α > 0, and W(x) = exp(− exp(¦x¦ϱ)), ϱ > 0." @default.
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- W2077377218 date "1985-08-01" @default.
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- W2077377218 title "Estimates of Freud-Christoffel functions for some weights with the whole real line as support" @default.
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- W2077377218 doi "https://doi.org/10.1016/0021-9045(85)90086-3" @default.
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