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


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
    $$ \alpha \left( {\mu _t } \right) = \mu _{\alpha \cdot t} \,for\,all\,t \geqslant 0,\,for\;some\;\left( {\alpha ,\alpha } \right) \in \;Aut\left( {\Bbb G} \right) \times \left] {0,1} \right[;$$
    equivalently, the corresponding Lévy process (X t ) t≥0 is variant w.r.t space-time transformations,
    $$ \alpha ^{ - 1} \left( {X_{\alpha - t} } \right)\mathop = \limits^D X_t ,\;t \geqslant 0. $$


Convolution Semigroup Gelfand Pair Free Convolution Levy Process Outer Normalization 
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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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