Expansion into Clifford Prolate Spheroidal Wave Functions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915692859621376 |
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| author | Ghaffari, Hamed Baghal Souabni, Ahmed |
| author_facet | Ghaffari, Hamed Baghal Souabni, Ahmed |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20646 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Expansion into Clifford Prolate Spheroidal Wave Functions Ghaffari, Hamed Baghal Souabni, Ahmed General Mathematics 15A67, 15A66 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. |
| title | Expansion into Clifford Prolate Spheroidal Wave Functions |
| topic | General Mathematics 15A67, 15A66 |
| url | https://arxiv.org/abs/2512.20646 |