Potential Theory for Transient Convolution Semigroups

  • Christian Berg
  • Gunnar Forst
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 87)

Abstract

Let (µt)t>0 be a convolution semigroup on the LCA-group G, and let (P t )t>0 denote the induced Feller semigroup. It is often useful, in the study of (µt)t>0, to replace the potential operator \(N = \smallint _o^\infty {\text{ }}{{\text{P}}_s}ds{\text{ for (}}{{\text{P}}_t}{{\text{)}}_{t >0}}\) with the measure (if it exists)
$$\kappa = \int\limits_0^\infty {\mu _t dt.} $$

Keywords

Convolution Hunt Stein Proal 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • Christian Berg
    • 1
  • Gunnar Forst
    • 1
  1. 1.University of KøbenhavnKøbenhavnDenmark

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