Prof. Dr. Wolfgang Arendt, Universität Ulm: "Fractional Powers via the Dirichlet to Neumann Operator"
We show that each sectoriel operator A on Hilbert space leads to a well-posed Dirichlet-to-Neumann Problem with very precise regulariiy results.
This allows us to construct the fractional powers of A in a definitely unusual way.
If A is the Laplacian such a construction was done before in a very influential paper by Caffarelli and Silvestre (without proving well posedness).
W. Arendt, T. ter Elst, M. Warma: Fractional powers of sectorial operators via the Dirichlet-to-Neumann operator.arXiv:1608.05707vl. 2016
L. Caffarelli, L. Silvestre: An extensions problem related to the fractional Laplacian. Comm. Partial Diff. Equ. 32 (2007) 1245-1260
Einladender: M. Haase