Erdös-Turán mean convergence theorem for Lagrange interpolation at Lobatto points
نویسندگان
چکیده
منابع مشابه
Analytic Erdös-Turán conjectures and Erdös-Fuchs theorem
We consider and study formal power series, that we call supported series, with real coefficients which are either zero or bounded below by some positive constant. The sequences of such coefficients have a lot of similarity with sequences of natural numbers considered in additive number theory. It is this analogy that we pursue, thus establishing many properties and giving equivalent statements ...
متن کاملOn 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 ...
متن کاملOn Weighted Mean Convergence of Lagrange Interpolation for General Arrays
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 ...
متن کاملConvergence of Extended Lagrange Interpolation
The authors give a procedure to construct extended interpolation formulae and prove some uniform convergence theorems.
متن کاملA Rate for the Erdös-Turán Law
The Erdős-Turán law gives a normal approximation for the order of a randomly chosen permutation of n objects. In this paper, we provide a sharp error estimate for the approximation, showing that, if the mean of the approximating normal distribution is slightly adjusted, the error is of order log−1/2n. Combinatorics, Probability and Computing (1994) 3, 167-176 Copyright
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1986
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s000497270001025x