Extension problem and fractional operators: semigroups and wave equations

@article{Gal2012ExtensionPA,
  title={Extension problem and fractional operators: semigroups and wave equations},
  author={J. E. Gal{\'e} and Pedro J. Miana and P. Stinga},
  journal={Journal of Evolution Equations},
  year={2012},
  volume={13},
  pages={343-368}
}
  • J. E. Galé, Pedro J. Miana, P. Stinga
  • Published 2012
  • Mathematics
  • Journal of Evolution Equations
  • We extend results of Caffarelli–Silvestre and Stinga–Torrea regarding a characterization of fractional powers of differential operators via an extension problem. Our results apply to generators of integrated families of operators, in particular to infinitesimal generators of bounded C0 semigroups and operators with purely imaginary symbol. We give integral representations to the extension problem in terms of solutions to the heat equation and the wave equation. 
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