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

M. Sh. Shabozov   ; G. A. Yusupov

Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 4, pp. 315-327

Résumé

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 $$ \Bigg(\int_0^h\Omega_m^q(f^{(r)},t)\,dt\Bigg)^{1/q}\leq\Phi(h), $$ where $r,m\in\mathbb N$, $1/r$, $0$, $\Omega_m(f^{(r)},t)_2$ 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 $\Phi(0)=0$.

Détail

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

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