Isometric properties of the Hankel transformation in weighted Sobolev spaces
Integral Transforms and Special Functions
It is shown that the Hankel transformation H v acts in a class of weighted Sobolev spaces. Especially, the isometric mapping property of H v which holds on L ² is extended to spaces of arbitrary Sobolev order. The novelty in the approach consists in using techniques developed by B.-W. Schulze and others to treat the half-line as a manifold with a conical singularity at r = 0. This is achieved by pointing out a connection between the Hankel transformation and the Mellin transformation. The procedure proposed leads at the same time to a short proof of the Hankel inversion formula. An application to the existence and higher regularity of solutions, including their asymptotics, to the 1+1 dimensional edge-degenerate wave equation is given.
Taylor & Francis
Hayrapetyan, Ruben G. and Witt, Ingo, "Isometric properties of the Hankel transformation in weighted Sobolev spaces" (2001). Mathematics Publications. 89.