In the hyperbolic disc (or more generally in real hyperbolic spaces) we consider the horospherical Radon transform R and the geodesic Radon transform X. Composition with their respective dual operators yields two convolution operators on the disc (with respect to the hyperbolic measure). We describe their convolution kernels in comparison with those of the corresponding operators on a homogeneous tree T, separately studied as acting on functions on the vertices or on the edges. This leads to a new theory of spherical functions and Radon inversion on the edges of a tree.

Radon transforms in hyperbolic spaces and their discrete counterparts / Casadio Tarabusi, Enrico; Picardello, Massimo A.. - In: COMPLEX ANALYSIS AND OPERATOR THEORY. - ISSN 1661-8254. - 15:(2020). [10.1007/s11785-020-01055-6]

Radon transforms in hyperbolic spaces and their discrete counterparts

Casadio Tarabusi, Enrico
;
2020

Abstract

In the hyperbolic disc (or more generally in real hyperbolic spaces) we consider the horospherical Radon transform R and the geodesic Radon transform X. Composition with their respective dual operators yields two convolution operators on the disc (with respect to the hyperbolic measure). We describe their convolution kernels in comparison with those of the corresponding operators on a homogeneous tree T, separately studied as acting on functions on the vertices or on the edges. This leads to a new theory of spherical functions and Radon inversion on the edges of a tree.
2020
Real hyperbolic spaces; homogeneous trees; Radon transform; X-ray transform; convolution operators; horospheres; spherical functions on trees; Plancherel measure
01 Pubblicazione su rivista::01a Articolo in rivista
Radon transforms in hyperbolic spaces and their discrete counterparts / Casadio Tarabusi, Enrico; Picardello, Massimo A.. - In: COMPLEX ANALYSIS AND OPERATOR THEORY. - ISSN 1661-8254. - 15:(2020). [10.1007/s11785-020-01055-6]
File allegati a questo prodotto
File Dimensione Formato  
CasadioTarabusi_Radon-transforms_2020.pdf

accesso aperto

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 600.84 kB
Formato Adobe PDF
600.84 kB Adobe PDF

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1434954
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact