Mean Convergence of Lagrange Interpolation. III
نویسندگان
چکیده
منابع مشابه
On Mean Convergence of Lagrange Interpolation for General Arrays
For n 1, let fxjngnj=1 be n distinct points in a compact set K R and let Ln[ ] denote the corresponding Lagrange Interpolation operator. Let v be a suitably restricted function on K. What conditions on the array fxjng1 j n; n 1 ensure the existence of p > 0 such that lim n!1 k (f Ln[f ]) v kLp(K)= 0 for every continuous f :: K ! R ? We show that it is necessary and su cient that there exists r ...
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For n 1, let fxjngnj=1 be n distinct points and let Ln[ ] denote the corresponding Lagrange Interpolation operator. Let W : R ! [0;1). What conditions on the array fxjng1 j n; n 1 ensure the existence of p > 0 such that lim n!1 k (f Ln[f ])W b kLp(R)= 0 for every continuous f : R ! Rwith suitably restricted growth, and some weighting factor ? We obtain a necessary and su¢ cient condition for ...
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The authors give a procedure to construct extended interpolation formulae and prove some uniform convergence theorems.
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Quadrature convergence of the extended Lagrange interpolant L2n+1f for any continuous function f is studied, where the interpolation nodes are the n zeros τi of an orthogonal polynomial of degree n and the n+ 1 zeros τ̂j of the corresponding “induced” orthogonal polynomial of degree n + 1. It is found that, unlike convergence in the mean, quadrature convergence does hold for all four Chebyshev w...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1984
ISSN: 0002-9947
DOI: 10.2307/1999259