Zero-Distribution of a Class of Finite Fourrier Transforms

摘要

Sufficient conditions the entire functions (*) E(F; z) = ∫_(-1)~1 F(t) exp(izt) dt to have finite many zeros outside a region of the kind S(σ) = {z = x + iy: -∞ < x < ∞, |y| < (1 + |x|)~(-σ),0 < σ < ∞} are proposed provided the complex function F ∈ L(-1,1） is such that either F(-t) = F(t), or F(-t) = -F(t), - 1 ≤ t ≤ 1. Asymptotics of the zeros of entire functions of the kind (*), having only real zeros, is studied.