Positive definiteness of piecewise-linear function

Let α∈(0,1), h∈R and let fα,h be an even function with the properties: fα,h(x)=0 for x∈(1,+∞), fα,h is linear over the intervals [0,α] and [α,1], fα,h(0)=1, fα,h(α)=h, and fα,h(1)=0. In this paper we prove that fα,h is positive definite on R⟺m(α)≤h≤1−α, where m(α)=0 if 1/α∉N, and m(α)=−α if 1/α∈N.