Isometric properties of the Hankel Transformation in weighted sobolev spaces
- It is shown that the Hankel transformation Hsub(v) acts in a class of weighted Sobolev spaces. Especially, the isometric mapping property of Hsub(v) which holds on L²(IRsub(+),rdr) 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 Rsub(+) 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-degenerated wave equation is given.
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