Addition to Polya's theorem on zeros of Fourier sine-transform

G. Polya described in [1] the distribution of zeros of the function V(z) = integral(0)(1) f(t) sin zt,dt f is an element of L(0,1) under assumptions that f(t) is positive, increasing, convex function in interval (0, 1), and f(0 + 0) = 0. The condition f (0 + 0) = 0 is essential for the Polya proof. Our aim is to study the distribution of zeros of V(z) when this condition is omitted.