J. Austral. Math. Soc.
72 (2002), 363-388|
Vector valued mean-periodic functions on groups
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
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
, we define the notion of convolution
. A function
is called mean-periodic if there exists a
In this paper we analyse the following questions:|
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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