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Trudy Inst. Mat. i Mekh. UrO RAN, 2012, Volume 18, Number 4, Pages 315–327 (Mi timm889)  

On the exact values of mean $\nu$-widths of some classes of entire functions

M. Sh. Shabozova, G. A. Yusupovb

a Institute of Mathematics, Academy of Sciences of Republic of Tajikistan
b Tajik National University

Abstract: We find the exact values of various $\nu$-widths for some classes of functions $f\in L_2^{(r)}(\mathbb R)$ differentiable on the axis $\mathbb R=(-\infty;+\infty)$ and satisfying the condition
$$ (\int_0^h\Omega_m^q(f^{(r)},t) dt)^{1/q}\leq\Phi(h), $$
where $r,m\in\mathbb N$, $1/r<q\leq2$, $0<h\le\pi$, $\Omega_m(f^{(r)},t)_2$ is the generalized modulus of continuity of $m$th order of the derivative $f^{(r)}\in L_2(\mathbb R)$, and $\Phi(t)$ is an arbitrary continuous function increasing on $t\ge0$ and such that $\Phi(0)=0$.

Keywords: spaces of measurable function, entire functions of exponential type $\sigma$, modulus of continuity of $m$th order, exact constant.

Full text: PDF file (214 kB)
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Document Type: Article
UDC: 517.5
Received: 23.11.2011

Citation: M. Sh. Shabozov, G. A. Yusupov, “On the exact values of mean $\nu$-widths of some classes of entire functions”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 4, 2012, 315–327

Citation in format AMSBIB
\Bibitem{ShaYus12}
\by M.~Sh.~Shabozov, G.~A.~Yusupov
\paper On the exact values of mean $\nu$-widths of some classes of entire functions
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2012
\vol 18
\issue 4
\pages 315--327
\mathnet{http://mi.mathnet.ru/timm889}
\elib{http://elibrary.ru/item.asp?id=18126492}


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