Wave extension problem for the fractional Laplacian
Journal article, 2015

We show that the fractional Laplacian can be viewed as a Dirichlet-to-Neumann map for a degenerate hyperbolic problem, namely, the wave equation with an additional diffusion term that blows up at time zero. A solution to this wave extension problem is obtained from the Schrodinger group by means of an oscillatory subordination formula, which also allows us to find kernel representations for such solutions. Asymptotics of related oscillatory integrals are analysed in order to determine the correct domains for initial data in the general extension problem involving non-negative self-adjoint operators. An alternative approach using Bessel functions is also described.


Mikko Kemppainen

University of Helsinki

Peter Sjögren

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

José Luis Torrea

Universidad Autonoma de Madrid (UAM)

Discrete and Continuous Dynamical Systems

1078-0947 (ISSN)

Vol. 35 10 4905-4929


Basic sciences

Subject Categories

Mathematical Analysis



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