Journal of Evolution Equations

, Volume 9, Issue 1, pp 171–195 | Cite as

Unbounded functional calculus for bounded groups with applications

  • Boris Baeumer
  • Markus Haase
  • Mihály Kovács
Open Access


In this paper, we develop the unbounded extension of the Hille–Phillips functional calculus for generators of bounded groups. Mathematical applications include the generalised Lévy–Khintchine formula for subordinate semigroups, the analyticity of semigroups generated by fractional powers of group generators, where the power is not an odd integer, and a shifted abstract Grünwald formula. We also give an application of the theory to subsurface hydrology, modeling solute transport on a regional scale using fractional dispersion along flow lines.

Mathematics Subject Classification (2000)

47A60 47D03 26A33 


Subordination Fractional powers Operational calculus Functional calculus Fractional calculus Stable laws Fractional derivatives 


Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2009

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of OtagoDunedinNew Zealand
  2. 2.Delft Institute of Applied MathematicsDelft University of TechnologyDelftThe Netherlands

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