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INTEGRABLE MEAN PERIODIC-FUNCTIONS ON LOCALLY COMPACT ABELIAN-GROUPS

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Title INTEGRABLE MEAN PERIODIC-FUNCTIONS ON LOCALLY COMPACT ABELIAN-GROUPS
 
Creator RANA, IK
NAVADA, KG
 
Subject locally compact abelian groups
mean periodic functions on groups
almost periodic functions
character group
annihilator
fourier transform
 
Description Let G be a locally compact abelian group with a Haar measure lambda(G). A function f on G is said to be mean-periodic if there exists a nonzero finite regular measure mu of compact support on G such that f*mu = 0. It is known that there exist no nontrivial integrable mean periodic functions on R(n) . We show that there exist nontrivial integrable mean periodic functions on G provided G has nontrivial proper compact subgroups. Let f is-an-element-of L1 (G) be mean periodic with respect to a nonzero finite measure mu of compact support. If mu(G) not-equal 0 and lambda(G) (SUPP(mu)) > 0 , then there exists a compact subgroup K of G such that f*lambda(K) = 0, i.e., f is mean periodic with respect to lambda(K) , where lambda(K) denotes the normalized Haar measure of K. When G is compact, abelian and meterizable, we show that there exists continuous (hence integrable and almost periodic) functions on G that arc not mean periodic.
 
Publisher AMER MATHEMATICAL SOC
 
Date 2011-07-16T18:39:16Z
2011-12-26T12:49:54Z
2011-12-27T05:35:43Z
2011-07-16T18:39:16Z
2011-12-26T12:49:54Z
2011-12-27T05:35:43Z
1993
 
Type Article
 
Identifier PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 117(2), 405-410
0002-9939
http://dx.doi.org/10.2307/2159175
http://dspace.library.iitb.ac.in/xmlui/handle/10054/4498
http://hdl.handle.net/10054/4498
 
Language en