Revisit on the Slepian concentration problem of the spherical Fourier-Bessel setup
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916396908150784 |
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| author | Huang, Xinpeng |
| author_facet | Huang, Xinpeng |
| contents | In this paper, we will revisit the Slepian spatiospectral concentration problem for the spherical Fourier-Bessel band-limited spaces introduced for 3-D domain, and discuss its general form in $\mathbb{R}^d$, $d\geq 2$. In particular, we investigate the bimodal distribution of eigenvalues of the concentration operators and give an asymptotic characterization of the Shannon number given a linear relation between the Bessel bandwidth and spherical harmonic bandwidth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17444 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Revisit on the Slepian concentration problem of the spherical Fourier-Bessel setup Huang, Xinpeng Functional Analysis In this paper, we will revisit the Slepian spatiospectral concentration problem for the spherical Fourier-Bessel band-limited spaces introduced for 3-D domain, and discuss its general form in $\mathbb{R}^d$, $d\geq 2$. In particular, we investigate the bimodal distribution of eigenvalues of the concentration operators and give an asymptotic characterization of the Shannon number given a linear relation between the Bessel bandwidth and spherical harmonic bandwidth. |
| title | Revisit on the Slepian concentration problem of the spherical Fourier-Bessel setup |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2402.17444 |