Integral Equations and Operator Theory

, Volume 26, Issue 1, pp 1–13 | Cite as

The convolution equation of Choquet and Deny on nilpotent groups

  • Cho-Ho Chu
  • Titus Hilberdink


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.

1991 Mathematics Subject Classification

Primary 43A05 46A55 45E10 45N05 Secondary 22E25 


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Copyright information

© Birkhäuser Verlag 1996

Authors and Affiliations

  • Cho-Ho Chu
    • 1
  • Titus Hilberdink
    • 1
  1. 1.Goldsmiths CollegeUniversity of LondonLondonEngland

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