The $L^p$ convergence of Fourier series on triangular domains
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866910306673885184 |
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| author | Babb, Ryan Luis Acosta |
| author_facet | Babb, Ryan Luis Acosta |
| contents | We prove $L^p$ norm convergence for (appropriate truncations of) the Fourier series arising from the Dirichlet Laplacian eigenfunctions on three types of triangular domains in $\mathbb{R}^2$: (i) the 45-90-45 triangle, (ii) the equilateral triangle and (iii) the hemiequilateral triangle (i.e. half an equilateral triangle cut along its height). The limitations of our argument to these three types are discussed in light of Lamé's Theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_07641 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The $L^p$ convergence of Fourier series on triangular domains Babb, Ryan Luis Acosta Classical Analysis and ODEs Analysis of PDEs Functional Analysis 42B08 (Primary) 42B05, 34L10, 35P10, 42A10 (Secondary) We prove $L^p$ norm convergence for (appropriate truncations of) the Fourier series arising from the Dirichlet Laplacian eigenfunctions on three types of triangular domains in $\mathbb{R}^2$: (i) the 45-90-45 triangle, (ii) the equilateral triangle and (iii) the hemiequilateral triangle (i.e. half an equilateral triangle cut along its height). The limitations of our argument to these three types are discussed in light of Lamé's Theorem. |
| title | The $L^p$ convergence of Fourier series on triangular domains |
| topic | Classical Analysis and ODEs Analysis of PDEs Functional Analysis 42B08 (Primary) 42B05, 34L10, 35P10, 42A10 (Secondary) |
| url | https://arxiv.org/abs/2202.07641 |