Addition to pólya's theorem on zeros of fourier sine-transforms

Abstract

G. Pólya described in [1] the distribution of zeros of the function

under assumptions that f(t) is positive, increasing, convex function in interval (0,1), and f(0 + 0) = 0. The conditions f(0 + 0) = 0 is essential for the Pólya proof. Our aim is to study the distribution of zeros of V(z) when this condition is omitted.

Keywords:

• Fourier transforms
• zeros of entire functions

MSC(1991):

• 30D10
• 30D20
• 42A38