2023/10/22 by Hendrik De Bie, De Bie, Hendrik, Pan Lian +3
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2310.14229
openalex publication_date 2023/10/22 · openalex created_date 2023/10/25 · openalex updated_date 2026/07/28
In this paper, we study the pointwise bounds for the kernel of the (κ, a)-generalized Fourier transform with κ≡0, introduced by Ben Saïd, Kobayashi and Orsted. We present explicit formulas for the case a=4, which show that the kernels can exhibit polynomial growth. Subsequently, we provide a polynomial bound for the even dimensional kernel for this transform, focusing on the cases with finite order. Furthermore, by utilizing an estimation for the Prabhakar function, it is found that the (0,a)-generalized Fourier kernel is bounded by a constant when a>1 and m≥ 2, except within an angular domain that diminishes as a → ∞. As a byproduct, we prove that the (0, 2ℓ/n)-generalized Fourier kernel is uniformly bounded, when m=2 and ℓ, n∈ ℕ.