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Asymptotics for the Radon transform on hyperbolic spaces

Annotation

Let G/H be a hyperbolic space over R; C or H; and let K be a maximal compact subgroup of G. Let D denote a certain explicit invariant differential operator, such that the non-cuspidal discrete series belong to the kernel of D. For any L^2-Schwartz function f on G/H we prove that the Abel transform A(Df) of Df is a Schwartz function. This is an extension of a result established in [2] for K-finite and K∩H-invariant functions.

Keywords

hyperbolic spaces; Radon transform; cuspidal discrete series; Abel transform

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DOI

10.20310/2686-9667-2019-24-127-241-251

UDC

517.986.66

Pages

241-251

References

[1] N. B. Andersen, M. Flensted-Jensen and H. Schlichtkrull, “Cuspidal discrete series for semisimple symmetric spaces”, Journal of Functional Analysis, 263:8 (2012), 2384–2408. [2] N. B. Andersen, M. Flensted-Jensen, “Cuspidal discrete series for projective hyperbolic spaces”, Contemporary Mathematics. V. 598: Geometric Analysis and Integral Geometry, Amer Mathematical Society, Providence, 2013, 59–75.

Received

2019-05-21

Section of issue

Scientific articles

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