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Zbl 1031.42004
Zhang, Chuanyi
A characterization of pseudo almost periodic functions in Fourier analysis.
(English)
[J] Acta Anal. Funct. Appl. 4, No.2, 110-114 (2002). ISSN 1009-1327

A function $f$, defined on $\bbfR$ and taking complex values, is called pseudo almost periodic if it can be represented in the form $f= g+h$, with $g$ almost periodic (Bohr) and $h$ such that $\lim(2t)^{-1} \int^t_{-t} h(x) dx= 0$, as $t\to\infty$. The characterization given by the author is: A function $f$, continuous and bounded on $R$, with complex values, is pseudo almost periodic if and only if there exists an almost periodic function $g$ with the same Fourier series, while $f$ satisfies the Parseval's equality.
[C.Corduneanu (Arlington)]
MSC 2000:
*42A75 Periodic functions and generalizations

Keywords: pseudo almost periodic function

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