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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

Potential Theory Convex Cone Convolution Kernel Compact Neighbourhood Bernstein Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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