Remarks on the $L^p$ convergence of Bessel–Fourier series on the disc
The $L^p$ convergence of eigenfunction expansions for the Laplacian on planar domains is largely unknown for $p\ne 2$. After discussing the classical Fourier series on the 2-torus, we move onto the disc, whose eigenfunctions are explicitly computable as products of trigonometric and Bessel functions...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2023-10-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.464/ |
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| Summary: | The $L^p$ convergence of eigenfunction expansions for the Laplacian on planar domains is largely unknown for $p\ne 2$. After discussing the classical Fourier series on the 2-torus, we move onto the disc, whose eigenfunctions are explicitly computable as products of trigonometric and Bessel functions. We summarise a result of Balodis and Córdoba regarding the $L^p$ convergence of the Bessel–Fourier series in the mixed norm space $L^p_{\mathrm{rad}}(L^2_{\mathrm{ang}})$ on the disk for the range $\tfrac{4}{3} |
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| ISSN: | 1778-3569 |