Range of the horocyclic Radon transform on trees

Enrico Casadio Tarabusi; Joel M. Cohen; Flavia Colonna

Annales de l'institut Fourier (2000)

  • Volume: 50, Issue: 1, page 211-234
  • ISSN: 0373-0956

Abstract

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In this paper we study the Radon transform R on the set ℋ of horocycles of a homogeneous tree T , and describe its image on various function spaces. We show that the functions of compact support on ℋ that satisfy two explicit Radon conditions constitute the image under R of functions of finite support on T . We extend these results to spaces of functions with suitable decay on T , whose image under R satisfies corresponding decay conditions and contains distributions on ℋ that are not defined pointwise. We also show that R is one-to-one on these spaces. Formulas are expressed in an invariant fashion in terms of a measure on ℋ preserved by the full automorphism group of T .

How to cite

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Tarabusi, Enrico Casadio, Cohen, Joel M., and Colonna, Flavia. "Range of the horocyclic Radon transform on trees." Annales de l'institut Fourier 50.1 (2000): 211-234. <http://eudml.org/doc/75414>.

@article{Tarabusi2000,
abstract = {In this paper we study the Radon transform $R$ on the set $\{\cal H\}$ of horocycles of a homogeneous tree $T$, and describe its image on various function spaces. We show that the functions of compact support on $\{\cal H\}$ that satisfy two explicit Radon conditions constitute the image under $R$ of functions of finite support on $T$. We extend these results to spaces of functions with suitable decay on $T$, whose image under $R$ satisfies corresponding decay conditions and contains distributions on $\{\cal H\}$ that are not defined pointwise. We also show that $R$ is one-to-one on these spaces. Formulas are expressed in an invariant fashion in terms of a measure on $\{\cal H\}$ preserved by the full automorphism group of $T$.},
author = {Tarabusi, Enrico Casadio, Cohen, Joel M., Colonna, Flavia},
journal = {Annales de l'institut Fourier},
keywords = {Radon transform; homogeneous trees; horocycles; range characterization; distributions},
language = {eng},
number = {1},
pages = {211-234},
publisher = {Association des Annales de l'Institut Fourier},
title = {Range of the horocyclic Radon transform on trees},
url = {http://eudml.org/doc/75414},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Tarabusi, Enrico Casadio
AU - Cohen, Joel M.
AU - Colonna, Flavia
TI - Range of the horocyclic Radon transform on trees
JO - Annales de l'institut Fourier
PY - 2000
PB - Association des Annales de l'Institut Fourier
VL - 50
IS - 1
SP - 211
EP - 234
AB - In this paper we study the Radon transform $R$ on the set ${\cal H}$ of horocycles of a homogeneous tree $T$, and describe its image on various function spaces. We show that the functions of compact support on ${\cal H}$ that satisfy two explicit Radon conditions constitute the image under $R$ of functions of finite support on $T$. We extend these results to spaces of functions with suitable decay on $T$, whose image under $R$ satisfies corresponding decay conditions and contains distributions on ${\cal H}$ that are not defined pointwise. We also show that $R$ is one-to-one on these spaces. Formulas are expressed in an invariant fashion in terms of a measure on ${\cal H}$ preserved by the full automorphism group of $T$.
LA - eng
KW - Radon transform; homogeneous trees; horocycles; range characterization; distributions
UR - http://eudml.org/doc/75414
ER -

References

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