Abstract
G. Choquet and J. Deny have characterized the positive solutions μ of the convolution equation σ*μ=μ of measures on locally compact abelian groups, for a given positive measure σ. By elementary methods, we extend their characterization to locally compact nilpotent groups which complements the various existing results on the equation, and we work out the solutions μ explicitly for the Heisenberg groups and some nilpotent matrix groups, by finding all the exponential functions on these groups.
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Chu, CH., Hilberdink, T. The convolution equation of Choquet and Deny on nilpotent groups. Integr equ oper theory 26, 1–13 (1996). https://doi.org/10.1007/BF01229501
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DOI: https://doi.org/10.1007/BF01229501