Isometric properties of the Hankel Transformation in weighted sobolev spaces

• Main Authors: Airapetyan, Ruben, Witt, Ingo
• Format: Others
• Language: English
• Published: Universität Potsdam 1997
• Subjects: Mathematics
• Online Access: http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25001; http://opus.kobv.de/ubp/volltexte/2008/2500/

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.