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Lookup NU author(s): Professor Barry Johnson
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For a probability measure σ on a locally compact group G which is not supported on any proper closed subgroup, an element F of L∞(G) is called σ-harmonic if (latin small letter esh) F(st)dσ(t) = F(s) for almost all s in G. Constant functions are σ-harmonic and it is known that for abelian G all σ -harmonic functions are constant. For other groups it is known that non constant σ-harmonic functions exist and the question of whether such functions exist on nilpotent groups is open, though a number of partial results are known. We show that for nilpotent groups of class 2 there are no non constant σ-harmonic functions. Our methods also enable us to give new proofs of results similar to the known partial results.
Author(s): Johnson BE
Publication type: Article
Publication status: Published
Journal: Integral Equations and Operator Theory
Year: 2001
Volume: 40
Issue: 4
Pages: 454-464
Print publication date: 01/01/2001
ISSN (print): 0378-620X
ISSN (electronic): 1420-8989
Publisher: Birkhaeuser Verlag AG
URL: http://dx.doi.org/10.1007/BF01198140
DOI: 10.1007/BF01198140
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