Product formula for one-dimensional (k,a)-generalized Fourier kernel

2023/01/16 by Béchir Amri, Amri, Bechir
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2301.06587

openalex publication_date 2023/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, a product formula for the one-dimensional (k,a)-generalized Fourier kernel is given for k≥0, a>0 and 2k>a-1, extending the special case when a=(2)/(n), n∈ ℕ.

Related

• Bounds for the kernel of the (κ, a)-generalized Fourier transform
• Explicit formulas for the Dunkl dihedral kernel and the (κ, a)-generalized Fourier kernel
• A positive product formula of integral kernels of k-Hankel transforms
• On the kernel of the (κ,a)-generalized Fourier transform
• The kernel of the generalized Clifford-Fourier transform and its generating function