Let E = ∪ from ∞ to n = - ∞ of [a_n,b_n], where the a_n and b_n satisfy the following relations: 0 < c_1 ≤ b_n - a_n ≤ c_2 and 0 < c_3 ≤ a_(n + 1) - b_n ≤ c_4, n = 0, ±1, ±2. Denote by B_σ the class of all entire functions of exponential type ≤ σ bounded on the real axis. Under certain assumptions on the rate of approximation on E of a bounded function f by functions in B_σ (σ varies), we get some information about the smoothness of f. Bibliography: 4 titles.
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