TY - JOUR
T1 - Isometric properties of the Hankel transformation in weighted Sobolev spaces
AU - Hayrapetyan, Ruben G.
AU - Witt, Ingo
PY - 2001/6/1
Y1 - 2001/6/1
N2 - 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.
AB - 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.
UR - https://digitalcommons.kettering.edu/mathematics_facultypubs/89
UR - https://www.tandfonline.com/doi/abs/10.1080/10652460108819313
U2 - 10.1080/10652460108819313
DO - 10.1080/10652460108819313
M3 - Article
VL - 11
JO - Integral Transforms and Special Functions
JF - Integral Transforms and Special Functions
ER -