IJPAM: Volume 71, No. 1 (2011)

EBERLEIN ALMOST PERIODIC FUNCTIONS
THAT ARE NOT PSEUDO ALMOST PERIODIC

Bolis Basit$^1$, Hans Günzler$^2$
$^1$School of Mathematical Sciences
Monash University
P.O. Box 28M, Victoria, 3800, AUSTRALIA
$^2$Mathematical Seminar der University of Kiel
Ludewig-Meyn-Str., 24098, Kiel, DEUTSCHLAND


Abstract. We construct Eberlein almost periodic functions $ f_j : J \to H$ so that $\vert\vert f_1(\cdot)\vert\vert$ is not ergodic and thus not Eberlein almost periodic and $\vert\vert f_2(.)\vert\vert$ is Eberlein almost periodic, but $f_1$ and $f_2$ are not pseudo almost periodic, the Parseval equation for them fails, where $J=\Rdb_+$ or $\Rdb$ and $H$ is a Hilbert space. This answers several questions posed by Zhang and Liu [18].

Received: April 11, 2011

AMS Subject Classification: 43A60, 42A16, 42A75, 42A99

Key Words and Phrases: Eberlein almost periodic, pseudo-almost periodic, Parseval equation

Download paper from here.


Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 71
Issue: 1