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- Author or Editor: J. Szabados x
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Abstract
We establish sufficient conditions on the parameter θ > 0 of the Cesàro means of Fourier-Jacobi series in spaces of locally continuous functions in order to have bounded weighted norm. For θ ≥ 1, a Stechkin type error estimate for the order of convergence will also be given.
Abstract
We consider the classical extremal problem of estimating norms of higher order derivatives of algebraic polynomials when their norms are given. The corresponding extremal problem for general polynomials in uniform norm was solved by A. A. Markov, while Bernstein found the exact constant in the Markov inequality for monotone polynomials. In this note we give Markov-type inequalities for higher order derivatives in the general class of k-monotone polynomials. In particular, in case of first derivative we find the exact solution of this extremal problem in both uniform and L 1-norms. This exact solution is given in terms of the largest zeros of certain Jacobi polynomials.
Эта общая теорема о на сыщении применяется к так называемым дискретн ым операторам свертки, в частности, с различным дискретны м вариантом интеграла Джексона, о ператоров Фейера-Коровкина и ин теграла Валле Пуссен а.
