Title
Isometric properties of the Hankel transformation in weighted Sobolev spaces
Document Type
Article
Publication Date
6-1-2001
Publication Title
Integral Transforms and Special Functions
Abstract
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.
Volume
11
Issue
3
First Page
201
Last Page
224
DOI
https://doi.org/10.1080/10652460108819313
ISSN
1476-8291
Rights
Taylor & Francis
Recommended Citation
Hayrapetyan, Ruben G. and Witt, Ingo, "Isometric properties of the Hankel transformation in weighted Sobolev spaces" (2001). Mathematics Publications. 89.
https://digitalcommons.kettering.edu/mathematics_facultypubs/89
