Let
W1 (G) = { x = G*y:yeL1 ,||y||1 \leqq 1} (L1 = L1 (R1 ))W_1 (G) = \{ x = G*y:y\varepsilon L_1 ,\parallel y\parallel _1 \leqq 1\} (L_1 = L_1 (R^1 ))
|
and
W10 (G) = { x = G*yeW1 (G), y ^1} .W_1^0 (G) = \{ x = G*y\varepsilon W_1 (G), y \bot 1\} .
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For each even function
G(t) (¦G
(v)(t)¦
/(1+t
2), v=0,1,...; t
R
1) such that its Fourier transform
g(t) is 4 times monotonous on [
, 
) and tends to zero as
t
, exact estimates of the best one-sided approximations by entire functions of exponential type
(
) are calculated for the classes
W
1
(G) and
W
1
0
(G) in
L
1-metric.