2021/08/12 by Sophie Mildenberger, Michael Quellmalz
Computer Science · Engineering · Mathematics · #Absolute convergence #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Convergence (economics) #Discrete Fourier series #Fourier analysis #Fourier series #Fourier transform #Function (biology) #Geometry #Mathematical analysis #Mathematics #Numerical methods in inverse problems #Pure mathematics #Series (stratigraphy) #Short-time Fourier transform #Smoothness #Sobolev space #Spherical harmonics #Spherical mean #Torus #cs.NA #math.FA #math.NA #msc:42B05 #msc:42C10 #msc:43A90 #msc:65T50
paper · pdf · doi:10.1007/s00041-022-09928-4
published as Journal of Fourier Analysis and Applications volume 28, Article number: 31 (2022)
arxiv created 2021/08/12 · openalex publication_date 2022/03/21 · arxiv updated 2022/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate analytic properties of the double Fourier sphere (DFS) method, which transforms a function defined on the two-dimensional sphere to a function defined on the two-dimensional torus. Then the resulting function can be written as a Fourier series yielding an approximation of the original function. We show that the DFS method preserves smoothness: it continuously maps spherical Hölder spaces into the respective spaces on the torus, but it does not preserve spherical Sobolev spaces in the same manner. Furthermore, we prove sufficient conditions for the absolute convergence of the resulting series expansion on the sphere as well as results on the speed of convergence.