Huygens’ principle and a Paley–Wiener type theorem on Damek–Ricci spaces

Francesca Astengo[1]; Bianca Di Blasio[2]

  • [1] Dipartimento di Matematica Via Dodecaneso 35 16146 Genova Italy
  • [2] Dipartimento di Matematica e Applicazioni Via Cozzi 53 20125 Milano Italy

Annales mathématiques Blaise Pascal (2010)

  • Volume: 17, Issue: 2, page 327-340
  • ISSN: 1259-1734

Abstract

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We prove that Huygens’ principle and the principle of equipartition of energy hold for the modified wave equation on odd dimensional Damek–Ricci spaces. We also prove a Paley–Wiener type theorem for the inverse of the Helgason Fourier transform on Damek–Ricci spaces.

How to cite

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Astengo, Francesca, and Di Blasio, Bianca. "Huygens’ principle and a Paley–Wiener type theorem on Damek–Ricci spaces." Annales mathématiques Blaise Pascal 17.2 (2010): 327-340. <http://eudml.org/doc/116355>.

@article{Astengo2010,
abstract = {We prove that Huygens’ principle and the principle of equipartition of energy hold for the modified wave equation on odd dimensional Damek–Ricci spaces. We also prove a Paley–Wiener type theorem for the inverse of the Helgason Fourier transform on Damek–Ricci spaces.},
affiliation = {Dipartimento di Matematica Via Dodecaneso 35 16146 Genova Italy; Dipartimento di Matematica e Applicazioni Via Cozzi 53 20125 Milano Italy},
author = {Astengo, Francesca, Di Blasio, Bianca},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Wave equation; Damek–Ricci space; Huygens' principle; wave equation; Damek-Ricci space; equipartition of energy; Paley-Wiener type theorem; Helgason Fourier transform},
language = {eng},
month = {7},
number = {2},
pages = {327-340},
publisher = {Annales mathématiques Blaise Pascal},
title = {Huygens’ principle and a Paley–Wiener type theorem on Damek–Ricci spaces},
url = {http://eudml.org/doc/116355},
volume = {17},
year = {2010},
}

TY - JOUR
AU - Astengo, Francesca
AU - Di Blasio, Bianca
TI - Huygens’ principle and a Paley–Wiener type theorem on Damek–Ricci spaces
JO - Annales mathématiques Blaise Pascal
DA - 2010/7//
PB - Annales mathématiques Blaise Pascal
VL - 17
IS - 2
SP - 327
EP - 340
AB - We prove that Huygens’ principle and the principle of equipartition of energy hold for the modified wave equation on odd dimensional Damek–Ricci spaces. We also prove a Paley–Wiener type theorem for the inverse of the Helgason Fourier transform on Damek–Ricci spaces.
LA - eng
KW - Wave equation; Damek–Ricci space; Huygens' principle; wave equation; Damek-Ricci space; equipartition of energy; Paley-Wiener type theorem; Helgason Fourier transform
UR - http://eudml.org/doc/116355
ER -

References

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