The Sets Of Positivity Of Sine Series With Monotone Coefficients

Abstract

We study the sums of nondegenerate sine series with monotone coefficients and consider the sets of positivity of such functions. We obtain the sharp lower estimate of the measure of such a set on $$[\pi/2, \pi]$$ and a new lower bound on its measure on $$[0,\pi]$$ . It is shown that the latter measure is at least $$\pi/2 + 0.24$$ and in the case of fulfilling special conditions it is at least $$2\pi/3$$ , which is an unimprovable estimate.