An extension of Szasz's theorem and its application

A classical result in signal theory is the completeness of the exponentials
\{ e^{-\mu_n x} \}
in
L_2
, the so-called Szasz's theorem. This paper generalizes Szasz's theorem by constructing broad classes of functions
g(x)
such that the set of functions
\{g(\mu_n x)\}
is complete in
L_2
. Application to the problem of alias-free sampling of stochastic processes is considered.