Abstract:
An investigation of measurable almost-everywhere finite functions
$\xi(t)$, $-\infty<t<+\infty$, for which
$$
\varphi_T^\xi(\tau_{(n)},\lambda_{(n)})=\frac1{2T}\int_{-T}^T\exp{i}\sum_{k=1}^n\lambda_k\xi(t-\tau_k)dt
$$
tends to an asymptotic characteristic function $\varphi_\infty^\xi(\tau_{(n)},\lambda_{(n)})$
when $T\to\infty$. Here $n$ is any positive integer and $\tau_{(n)}=(\tau_1,\tau_2,\dots,\tau_n)$ is arbitrary.
It is proved that the class of such functions $\xi(t)$ is larger than the class of Besicovich almost-periodic functions.
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