Extension problem and fractional operators: semigroups and wave equations

  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},
  • 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. 
    46 Citations
    Fractional powers of sectorial operators via the Dirichlet-to-Neumann operator
    • 24
    • PDF
    On the harmonic extension approach to fractional powers in Banach spaces
    • 2
    • PDF
    On extension problem, trace hardy and Hardy’s inequalities for some fractional Laplacians
    • 2
    • Highly Influenced
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    Symmetrization for fractional Neumann problems
    • 4
    • PDF
    Fractional elliptic problems with nonlinear gradient sources and measures
    • PDF


    Integrated Semigroups and Related Partial Differential Equations
    • 17
    Harnack's inequality for fractional nonlocal equations
    • 23
    • PDF
    Extension Problem and Harnack's Inequality for Some Fractional Operators
    • 307
    • PDF
    One-parameter groups of regular quasimultipliers
    • 24
    An Extension Problem Related to the Fractional Laplacian
    • 1,830
    • Highly Influential
    • PDF
    Laplace Transforms and α-Times Integrated Semigroups
    • 67
    spectra of pseudodifferential operators generating integrated semigroups
    • 15
    • PDF