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Epilogue

  • Wilfried Hazod
  • Eberhard Siebert
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 531)

Abstract

Starting with equivalent descriptions of (semi-) stability in the classical set-up, our investigations in the preceding chapters followed the scheme described below:
  1. (I)
    Semistable continous convolution semigroup μ• are defined by the relation
    $$ \alpha \left( {\mu _t } \right) = \mu _{\alpha \cdot t} \,for\,all\,t \geqslant 0,\,for\;some\;\left( {\alpha ,\alpha } \right) \in \;Aut\left( {\Bbb G} \right) \times \left] {0,1} \right[;$$
    (3.8.1)
    equivalently, the corresponding Lévy process (X t ) t≥0 is variant w.r.t space-time transformations,
    $$ \alpha ^{ - 1} \left( {X_{\alpha - t} } \right)\mathop = \limits^D X_t ,\;t \geqslant 0. $$
    (3.8.2)
     

Keywords

Convolution Semigroup Gelfand Pair Free Convolution Levy Process Outer Normalization 
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 Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Wilfried Hazod
    • 1
  • Eberhard Siebert
  1. 1.Mathematical DepartmentUniversity of DortmundDortmundGermany

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