J. Austral. Math. Soc.  72 (2002), 363-388
Vector valued mean-periodic functions on groups

 P. Devaraj   Department of Mathematics   Indian Institute of Technology   Powai, Mumbai-76   PIN-400076   India  devaraj@math.iitb.ac.in
and
 Inder K. Rana   Department of Mathematics   Indian Institute of Technology   Powai, Mumbai-76   PIN-400076   India  ikr@math.iitb.ac.in

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 mean-periodic if there exists a non-trivial 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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