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Vector valued mean-periodic functions on groups

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Title Vector valued mean-periodic functions on groups
 
Creator DEVARAJ, P
RANA, IK
 
Subject convolution of vector valued functions
spectrum
vector valued mean-periodic functions
spectral synthesis
 
Description Let G be a locally compact Hausdorff abelian group and X be a complex Banach space. Let C(G, X) denote the space of all continuous functions f : G --> X, with the topology of uniform convergence on compact sets. Let X' denote the dual of X with the weak* topology. Let M,(G, X') denote the space of all X'-valued compactly supported regular measures of finite variation on G. For a function f is an element of C(G, X) and mu is an element of M-c(G, X'), we define the notion of convolution f * mu. A function f is an element of C(G, X) is called mean-periodic if there exists a non-trivial measure mu is an element of M-c(G, X') such that f * mu = 0. For mu is an element of M-c(G, X'), let M P (mu) = {f is an element of C(G, X) : f * mu = 0} and let M P (G, X) = boolean ORmu M P (mu). In this paper we analyse the following questions: Is M P (G, X) not equal null set? Is M P (G, X) not equal C(G, X)? Is M P (G, X) dense in C(G, X)? Is M P (mu) generated by 'exponential monomials' in it? We answer these questions for the groups G = R, the real line, and G = T, the circle group. Problems of spectral analysis and spectral synthesis for C(R, X) and C(T, X) are also analysed.
 
Publisher AUSTRALIAN MATHEMATICS PUBL ASSOC INC
 
Date 2011-07-18T21:50:49Z
2011-12-26T12:50:51Z
2011-12-27T05:37:00Z
2011-07-18T21:50:49Z
2011-12-26T12:50:51Z
2011-12-27T05:37:00Z
2002
 
Type Article
 
Identifier JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 72(), 363-388
1446-7887
http://dspace.library.iitb.ac.in/xmlui/handle/10054/5083
http://hdl.handle.net/10054/5083
 
Language en