A class of functions of a real variable |
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Authors: | Yu I Alimov |
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Institution: | 1. Ural Branch, Academy of Sciences of the USSR, USSR
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Abstract: | An investigation of measurable almost-everywhere finite functions ξ(t), -∞ $$\varphi _T^\xi (\tau _{(n)} , \lambda _{(n)} ) = \frac{1}{{2T}}\int_{ - T}^T {\exp i} \sum\nolimits_{k - 1}^n {\lambda _k \xi (t - \tau _k )dt} $$ tends to an asymptotic characteristic function? ∞ ξ (τ (n), λ(n)) when T → ∞. Here n is any positive integer and T(n)=(τ1; τ2, ..., τn) is arbitrary. It is proved that the class of such functions ξ(t) is larger than the class of Besicovich almost-periodic functions. |
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