Fourier series and approximation on hexagonal and triangular domains

2008/02/04 by Yuan Xu, Xu, Yuan
Mathematics · #41A25 #41A63 #42B08 #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials #math.CA #msc:41A25 #msc:41A63 #msc:42B08

paper · pdf · doi:10.48550/arxiv.0802.0316

19 pages, 2 figures

arxiv created 2008/02/04 · openalex publication_date 2008/02/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Several problems on Fourier series and trigonometric approximation on a hexagon and a triangle are studied. The results include Abel and Cesàro summability of Fourier series, degree of approximation and best approximation by trigonometric functions, both direct and inverse theorems. One of the objective of this study is to demonstrate that Fourier series on spectral sets enjoy a rich structure that allow an extensive theory for Fourier expansions and approximation.

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