Continuous wavelet transform on semisimple Lie groups and inversion of the Abel transform and its dual.

Trimèche, K.. "Continuous wavelet transform on semisimple Lie groups and inversion of the Abel transform and its dual.." Collectanea Mathematica 47.3 (1996): 231-268. <http://eudml.org/doc/40339>.

@article{Trimèche1996,
abstract = {In this work we define and study wavelets and continuous wavelet transform on semisimple Lie groups G of real rank l. We prove for this transform Plancherel and inversion formulas. Next using the Abel transform A on G and its dual A*, we give relations between the continuous wavelet transform on G and the classical continuous wavelet transform on Rl, and we deduce the formulas which give the inverse operators of the operators A and A*.},
author = {Trimèche, K.},
journal = {Collectanea Mathematica},
keywords = {Ondículas; Grupos de Lie; Algebras semisimples; Integrales abelianas; Transformación inversa; Análisis armónico; Convolución; Espacio dual; Transformada de Fourier; Plancherel formula; inversion formula; wavelets; continuous wavelet transform; semisimple Lie groups; Abel transform},
language = {eng},
number = {3},
pages = {231-268},
title = {Continuous wavelet transform on semisimple Lie groups and inversion of the Abel transform and its dual.},
url = {http://eudml.org/doc/40339},
volume = {47},
year = {1996},
}

TY - JOUR
AU - Trimèche, K.
TI - Continuous wavelet transform on semisimple Lie groups and inversion of the Abel transform and its dual.
JO - Collectanea Mathematica
PY - 1996
VL - 47
IS - 3
SP - 231
EP - 268
AB - In this work we define and study wavelets and continuous wavelet transform on semisimple Lie groups G of real rank l. We prove for this transform Plancherel and inversion formulas. Next using the Abel transform A on G and its dual A*, we give relations between the continuous wavelet transform on G and the classical continuous wavelet transform on Rl, and we deduce the formulas which give the inverse operators of the operators A and A*.
LA - eng
KW - Ondículas; Grupos de Lie; Algebras semisimples; Integrales abelianas; Transformación inversa; Análisis armónico; Convolución; Espacio dual; Transformada de Fourier; Plancherel formula; inversion formula; wavelets; continuous wavelet transform; semisimple Lie groups; Abel transform
UR - http://eudml.org/doc/40339
ER -