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

Collectanea Mathematica (1996)

- Volume: 47, Issue: 3, page 231-268
- ISSN: 0010-0757

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topTrimèche, 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 -

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