2025/12/13 by Hamed Baghal Ghaffari, Ghaffari, Hamed Baghal, Ahmed Souabni +1
Mathematics · #15A66 #15A67 #Algebraic and Geometric Analysis #FOS: Mathematics #General Mathematics (math.GM) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods
paper · doi:10.48550/arxiv.2512.20646
openalex publication_date 2025/12/13 · openalex created_date 2025/12/26 · openalex updated_date 2026/07/28
In this paper, we investigate the properties of Clifford prolate spheroidal wave functions (CPSWFs) through their associated eigenvalues. We prove that the expansion coefficients in CPSWFs series decay as both the order and the homogeneity degree increase. By establishing a precise connection between the radial CPSWFs and the eigenfunctions of the finite Hankel transform, we derive explicit and non-asymptotic bounds on the corresponding eigenvalues and transfer the spectral decay estimates to the Clifford setting. Consequently, we obtain super-exponential decay rates for the CPSWF expansion coefficients of band-limited Clifford-valued functions. Numerical experiments illustrate both the accuracy and the efficiency of these approximations.