The strong converse inequality for de la Vallée Poussin means on the sphere

Details The strong converse inequality for de la Vallée Poussin means on the sphere The strong converse inequality for de la Vallée Poussin means on the sphere

2011-05-20

arxiv.org/abs/1105.4062v1

Mathematics

Classical Analysis and ODEs

14 pages

Scientific paper

This paper discusses the approximation by de la Vall\'{e}e Poussin means $V_nf$ on the unit sphere. Especially, the lower bound of approximation is studied. As a main result, the strong converse inequality for the means is established. Namely, it is proved that there are constants $C_1$ and $C_2$ such that \begin{eqnarray*} C_1\omega(f,\frac{1}{\sqrt n})_p \leq \|V_{n}f-f\|_p \leq C_2\omega(f,\frac{1}{\sqrt n})_p \end{eqnarray*} for any $p$-th Lebesgue integrable or continuous function $f$ defined on the sphere, where $\omega(f,t)_p$ is the modulus of smoothness of $f$.

Affiliated with

Also associated with

No associations

Rating

The strong converse inequality for de la Vallée Poussin means on the sphere does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The strong converse inequality for de la Vallée Poussin means on the sphere, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The strong converse inequality for de la Vallée Poussin means on the sphere will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-649230