The Radon transform on
Authors:
D. I. Wallace and Ryuji Yamaguchi
Journal:
Trans. Amer. Math. Soc. 297 (1986), 305-318
MSC:
Primary 22E30; Secondary 44A15, 53C65
DOI:
https://doi.org/10.1090/S0002-9947-1986-0849481-7
MathSciNet review:
849481
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Let be
.
acts on the upper half-plane
by the Möbius transformation, providing
with the Riemannian metric structure along with the Laplacian,
. We study the integral transform along each geodesic.
acts on
, the space of all geodesics, in a natural way, providing
with its invariant measure and its own Laplacian. (
actually is a coset space of
.) Therefore the above transform can be viewed as a map from a suitable function space on
to a suitable function space on
. We prove a number of properties of this transform, including the intertwining properties with its Laplacians and its relation to the Fourier transforms.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1986-0849481-7
Article copyright:
© Copyright 1986
American Mathematical Society