Mathematics – Classical Analysis and ODEs
Scientific paper
2010-03-25
Mathematics
Classical Analysis and ODEs
28 pages, in Russian, Submitted to a East Journal on Approximations
Scientific paper
Nikol'skii known theorem for the kernels satisfying a condition $A^*_n$, is proved and for kernels from wider class. Explicit formulas for calculating the value of an approximation of classes $\W^{r, \beta}_{p, n} $ by convolution operators of special form are obtained. Here $ \beta\in\Z $, $r> 0 $, $n\in\N $, and $p=1 $ or $p =\infty $. As particular cases obtained explicit formulas for value of an approximation of the indicated classes generalized Abel-Poisson means, biharmonic operators of Poisson, Cesaro and Riesz means. In some cases for value of an approximation of the indicated classes asymptotic expansions on parameter are found. In case of natural $r$ some results have been obtained in works Nikol'skii, Nagy, Timan, Telyakovskii, Baskakov, Falaleev, Kharkevich and other mathematicians. Key words: Nikol'skii theorem, an approximation of classes of functions, Abel-Poisson means, biharmonic operators of Poisson, Riesz and Cesaro means, asymptotic expansion, multiply monotone function, Hurwitz function.
No associations
LandOfFree
Exact estimation of an approximation of some classes of differentiable functions by convolution operators 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 Exact estimation of an approximation of some classes of differentiable functions by convolution operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Exact estimation of an approximation of some classes of differentiable functions by convolution operators will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-556912