Информационная система "Конференции"

Abstracts

Approximation of functions and quadrature formulas

It is investigated the transcendential equation of unknown function $s$ begin{equation} label{1} intlimits_0^frac{1}{2}|B_m(x)|^s sign(B_m(x))dx=0, end{equation} where $B_m(x)$ --- the Bernoully polynomial of $m$ degree, $s=q-1,$ $p,qin(1,infty),$ $frac{1}{p}+frac{1}{q}=1.$ Solutions of this equation define, what sequences of quadrature formulae are asymptotically optimal in spaces $L_p^m(a,b)$ on dependence from degrees of summing of derivatives integrable functions. Number $s$ is a solution of equation (ref{1}) if and only if sequences of quadrature formulae with regular boundary layer are asymptotically optimal in $L_p^m(a,b), quad pin(1,infty).$ If $m$ is an odd number then Sobolev's formulae with regular boundary layer are asymptotically optimal in $L_p^m(a,b),$ $pin(1,infty),$ $-infty Note. Abstracts are published in author's edition

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