The $L^p$ convergence of Fourier series on triangular domains

Autor:	Babb, Ryan Luis Acosta
Rok vydání:	2022
Předmět:	Mathematics - Classical Analysis and ODEs Mathematics - Analysis of PDEs Mathematics - Functional Analysis 42B08 (Primary) 42B05 34L10 35P10 42A10 (Secondary)
Druh dokumentu:	Working Paper
DOI:	10.1017/S0013091523000226
Popis:	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 Lam\'e's Theorem. Comment: 21 pages, 6 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2202.07641 Zobrazit plný text záznamu View this record from Arxiv