The Measure of the Set of Zeros of the Sum of a Nondegenerate Sine Series with Monotone Coefficients in the Closed Interval [0, π]

Аннотация

Nonzero sine series with monotone coefficients tending to zero are considered. It is shown that the measure of the set of those zeros of such a series which belong to [0, π] cannot exceed π/3. Moreover, if this value is attained, then almost all zeros belong to the closed interval [2π/3, π].