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Inverse Approximation Theorem on an Infinite Union of Segments
Authors:N. A. Shirokov
Affiliation:(1) St.Petersburg State University, Russia
Abstract:Let 
$$bigcuplimits_{n = - infty }^infty {[a_n ,b_n ]} $$
, where the 
$$a_n $$
and 
$$b_n $$
satisfy the following relations: 
$$0 < c_1 leqslant b_n - a_n leqslant c_n $$
and 
$$0 < c_3 leqslant a_{n + 1} - b_n leqslant c_4 ,n = 0, pm 1, pm 2$$
. Denote by Bsgr the class of all entire functions of exponential type le sgr bounded on the real axis. Under certain assumptions on the rate of approximation on E of a bounded function f by functions in Bsgr (sgr varies), we get some information about the smoothness of f. Bibliography: 4 titles.
Keywords:
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