Abstract:
Schep proved that, for a piecewise linear function
with nodes at integer points,
positive definiteness on $\mathbb{R}$
is equivalent to positive definiteness
on $\mathbb{Z}$.
In this paper, a similar theorem
for an entire function of exponential type is proved,
and
a generalization Schep's theorem is obtained.
Keywords:positive definite functions, Fourier transform, Bochner–Khinchine theorem,
piecewise linear functions with equidistant nodes.
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