TY - JOUR
T1 - The linear canonical transforms associated with the Dunkl-type operator and its applications
AU - Mejjaoli, Hatem
AU - Poria, Anirudha
N1 - Publisher Copyright:
© 2025 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2025/7/10
Y1 - 2025/7/10
N2 - In this paper, we introduce the canonical Fourier transform associated with the Dunkl-type operator and study some of its important properties. We study the generalized translation operator and convolution product associated with this transform and present some of its basic properties. Next, at the heart of our investigation, we introduce and study the canonical wavelet transform associated with the generalized canonical Fourier transform. Nonetheless, special attention is paid to the applications of these new transforms.
AB - In this paper, we introduce the canonical Fourier transform associated with the Dunkl-type operator and study some of its important properties. We study the generalized translation operator and convolution product associated with this transform and present some of its basic properties. Next, at the heart of our investigation, we introduce and study the canonical wavelet transform associated with the generalized canonical Fourier transform. Nonetheless, special attention is paid to the applications of these new transforms.
KW - Generalized canonical Fourier transform
KW - generalized canonical wavelet transform
KW - Dunkl-type operator
KW - Chébli–Trimèche hypergroup
KW - translation operator
KW - convolution product
UR - https://www.scopus.com/pages/publications/105010523781
U2 - 10.1080/10652469.2025.2527167
DO - 10.1080/10652469.2025.2527167
M3 - Article
AN - SCOPUS:105010523781
SN - 1065-2469
SP - 1
EP - 40
JO - Integral Transforms and Special Functions
JF - Integral Transforms and Special Functions
ER -