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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2023-10-01
|
| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.464/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1825206258895945728 |
|---|---|
| author | Acosta Babb, Ryan Luis |
| author_facet | Acosta Babb, Ryan Luis |
| author_sort | Acosta Babb, Ryan Luis |
| collection | DOAJ |
| description | 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} |
| format | Article |
| id | doaj-art-ae36fb20ad484f1cabdceb1aaf576bca |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-10-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-ae36fb20ad484f1cabdceb1aaf576bca2025-02-07T11:09:55ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-10-01361G71075108010.5802/crmath.46410.5802/crmath.464Remarks on the $L^p$ convergence of Bessel–Fourier series on the discAcosta Babb, Ryan Luis0University of Warwick, United KingdomThe $L^p$ 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}https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.464/ |
| spellingShingle | Acosta Babb, Ryan Luis Remarks on the $L^p$ convergence of Bessel–Fourier series on the disc Comptes Rendus. Mathématique |
| title | Remarks on the $L^p$ convergence of Bessel–Fourier series on the disc |
| title_full | Remarks on the $L^p$ convergence of Bessel–Fourier series on the disc |
| title_fullStr | Remarks on the $L^p$ convergence of Bessel–Fourier series on the disc |
| title_full_unstemmed | Remarks on the $L^p$ convergence of Bessel–Fourier series on the disc |
| title_short | Remarks on the $L^p$ convergence of Bessel–Fourier series on the disc |
| title_sort | remarks on the l p convergence of bessel fourier series on the disc |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.464/ |
| work_keys_str_mv | AT acostababbryanluis remarksonthelpconvergenceofbesselfourierseriesonthedisc |