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Generalized wavelets and the generalized wavelet transform on $\mathbb{R}^d$ for the Heckman-Opdam theory

Amina Hassini|Khalifa Trimeche|Rayaane Maalaoui
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2016.06|한국수학논문집 (Korean Journal of Mathematics)|제24권 제2호|pp. 235-271|DOI http://dx.doi.org/10.11568/kjm.2016.24.2.235

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참고문헌

키워드

WaveletsHeckman-Opdam theoryGeneralized wavelet transform.
주제분류수학

초록

By using the Heckman-Opdam theory on $\mathbb{R}^d$ given in [20], we define and study in this paper, the generalized wavelets on $\mathbb{R}^d$ and the generalized wavelet transform on $\mathbb{R}^d$, and we establish their properties. Next, we prove for the generalized wavelet transform Plancherel and inversion formulas.

Abstract

By using the Heckman-Opdam theory on $\mathbb{R}^d$ given in [20], we define and study in this paper, the generalized wavelets on $\mathbb{R}^d$ and the generalized wavelet transform on $\mathbb{R}^d$, and we establish their properties. Next, we prove for the generalized wavelet transform Plancherel and inversion formulas.

참고문헌 (20)

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  18. Khalifa Trime`che, "THE POSITIVITY OF THE HYPERGEOMETRIC TRANSLATION OPERATORS ASSOCIATED TO THE CHEREDNIK OPERATORS AND THE HECKMAN-OPDAM THEORY ATTACHED TO THE ROOT SYSTEMS OF TYPE B2 AND C2", 한국수학논문집, 22(1), pp.1~28 (2014), 강원경기수학회[DOI]
  19. K.Trimeche, "Positivity of the transmutation operators and absolute continuity of their representing measures for a root system on Rd", Int. J. App. Math, 28(4), pp.427~453 (2015)
  20. K.Trimeche, "The harmonic analysis associated to the Heckman-Opdam theory and its application to a root system of type BCd", Preprint. Faculty of Sciences of Tunis, ~ (2015)

관련 논문AI추천

The Cherednik and the Gaussian Cherednik Windowed transforms on $\mathbb{R}^d$ in the W-invariant caseAmina Hassini, Khalifa Trimeche강원경기수학회 · 한국수학논문집2020 · 제28권 제4호The harmonic analysis associated to the Heckman-Opdam's theory and its application to a root system of type $BC_d$Khalifa Trimeche강원경기수학회 · 한국수학논문집2019 · 제27권 제1호Qualitative uncertainty principles for the inverse of the hypergeometric fourier transformHatem Mejjaoli강원경기수학회 · 한국수학논문집2015 · 제23권 제1호Spectral theorems associated to the Dunkl operatorsHatem Mejjaoli강원경기수학회 · 한국수학논문집2016 · 제24권 제4호Time-frequency analysis associated with k-Hankel-Wigner transformsMohamed Amine Boubatra대한수학회 · 대한수학회논문집2022 · 제37권 제2호Miyachi’s Theorem for the k-Hankel Transform on R^dMohamed Amine Boubatra경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2023 · 제63권 제3호

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