J. Austral. Math. Soc.
72 (2002), 363388  
Vector valued meanperiodic functions on groups
 
 
Abstract  
Let be a locally compact Hausdorff abelian group
and be a complex Banach space. Let
denote the space of all continuous functions
, with the topology of uniform convergence on
compact sets.
Let denote the dual of
with the weak* topology. Let
denote the space of all
valued compactly supported regular measures of
finite variation on
. For a function
and
, we define the notion of convolution
. A function
is called meanperiodic if there exists a
nontrivial measure
such that
. For
, let
and let
.
In this paper we analyse the following questions: Is ? Is ? Is dense in ? Is generated by `exponential monomials' in it? We answer these questions for the groups , the real line, and , the circle group. Problems of spectral analysis and spectral synthesis for and are also analysed.  
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