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Unitarization of the Horocyclic Radon Transform on Homogeneous Trees

by F. Bartolucci and F. De Mari and M. Monti

(Report number 2020-39)

Abstract
Following previous work in the continuous setup, we construct the unitarization of the horocyclic Radon transform on a homogeneous tree \(X\) and we show that it intertwines the quasi regular representations of the group of isometries of \(X\) on the tree itself and on the space of horocycles.

Keywords: homogeneous trees, horocyclic Radon transform, dual pairs, quasi regular representations

@Techreport{BDM20_912,
  author = {F. Bartolucci and F. De Mari and M. Monti},
  title = {Unitarization of the Horocyclic Radon Transform on Homogeneous Trees},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2020-39},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2020/2020-39.pdf },
  year = {2020}
}

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