论文标题
$ l^p $在三角形域上的傅立叶系列的收敛
The $L^p$ convergence of Fourier series on triangular domains
论文作者
论文摘要
我们证明了$ l^p $ norm融合（适当的截断）fourier系列是由dirichlet laplacian eigenfunctions在$ \ mathbb {r}^2 $：（i）45-90-45 triangle，（ii）equilian triangle，（ii）equilian triangle和（iii ii ii ii ii ii ii ii ii ii ii ii ii ii ii ii（iiii ii ii ii）中，在$ \ mathbb {r}^2 $中，在三种类型的三角形域上产生的傅立叶系列。等边三角形沿其高度切割）。根据Lamé的定理，讨论了我们论点对这三种类型的局限性。
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.
