TY  - INPR
A1  - Airapetyan, Ruben
A1  - Witt, Ingo
T1  - Isometric properties of the Hankel Transformation in weighted sobolev spaces
N2  - 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.
T3  - Preprint - (1997) 14 
Y1  - 2008
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/2298
UR  - https://nbn-resolving.org/urn:nbn:de:kobv:517-opus-25001
ER  -