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We prove the following theorem: Theorem: Let f(u) ∈ L(-π, π) and periodic with period 2π. Let a function P(u), tending to +∞ with u, and a sequence {p_n} be defined as follows in terms of p(u) monotonic decreasing and strictly positive for u > 0 (1.1) { P(u) - ∫_0^u p(x) dx ; p_n = p(u) } Then the assumption that for any δ, 0 < δ < π, (1.2) ∫_{1/n}^δ | 1/n ∏(u) | d/du [P(1/u)] du = o (p_0 + p_1 + ... + p_n ) as n → ∞ implies that the sequence {n(b_n cos n …
