Harmonic functions on nilpotent groups |
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Authors: | B E Johnson |
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Institution: | (1) Department of Mathematics, University of Newcastle, NE1 7RU Newcastle upon Tyne, England |
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Abstract: | For a probability measure on a locally compact groupG which is not supported on any proper closed subgroup, an elementF ofL
(G) is called -harmonic if F(st)d(t)=F(s), for almost alls inG. Constant functions are -harmonic and it is known that for abelianG all -harmonic functions are constant. For other groups it is known that non constant -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 -harmonic functions. Our methods also enable us to give new proofs of results similar to the known partial results. |
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Keywords: | Primary 43A05 Secondary 22D99 |
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