Информационная система "Конференции"

Abstracts

Approximation of functions and quadrature formulas

For fixed $s>1/2$ we study the sums of type $$ S_L(h)=sum_{0 neq x in L} frac{1}{((1+h^{-2}x_1^2)ldots(1+h^{-2}x_n^2))^s} eqno(*) $$ when $h to 0$. Here $x=(x_1,dots,x_n)$ and $L$ is a some $n$-dimensional lattice. The sums $(*)$ evaluate the norm of error functional $$ l_h:f mapsto intlimits_Omega f(x),dx- sum_{x^{(h)} in hL cap Omega} c_{x^{(h)}}f(x^{(h)}) $$ in some Sobolev's spaces. We construct the lattices $L$ such that the estimate $$ S_L(h)=O(h^{2ns}(log{h^{-1}})^{n-1}) $$ is true.

Note. Abstracts are published in author's edition

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