A double Fourier sphere method for \(d\)-dimensional manifolds

DOI10.1007/s43670-023-00064-8arXiv2301.06540MaRDI QIDQ6049830

Michael Quellmalz, Sophie Mildenberger

Publication date: 18 September 2023

Published in: Sampling Theory, Signal Processing, and Data Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2301.06540

zbMATH Keywords

Fourier seriesapproximation on manifoldsdouble Fourier sphere method

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Numerical methods for discrete and fast Fourier transforms (65T50) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Fourier series and coefficients in several variables (42B05)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A fast and accurate algorithm for spherical harmonic analysis on HEALPix grids with applications to the cosmic microwave background radiation
• Approximation properties of the double Fourier sphere method
• A fast algorithm for nonequispaced Fourier transforms on the rotation group
• An algorithm for the evaluation of multidimensional (direct and inverse) discrete Chebyshev transforms
• Commutative harmonic analysis IV: harmonic analysis in \(R^ n\). Transl from the Russian by J. Peetre
• A fast transform for spherical harmonics
• Computing Fourier transforms and convolutions on the 2-sphere
• Fast spherical Fourier algorithms.
• Numerical Fourier analysis
• Lectures on constructive approximation. Fourier, spline, and wavelet methods on the real line, the sphere, and the ball
• Estimates for local approximations of functions on differential manifold
• Parametric stitching for smooth coupling of subdomains with non-matching discretizations
• Approximation of functions over manifolds: a moving least-squares approach
• Ambient approximation on embedded submanifolds
• Isogeometric analysis using manifold-based smooth basis functions
• Fast and backward stable transforms between spherical harmonic expansions and bivariate Fourier series
• Introduction to Smooth Manifolds
• Scattered Data Interpolation on Embedded Submanifolds with Restricted Positive Definite Kernels: Sobolev Error Estimates
• On the Fourier Extension of Nonperiodic Functions
• A combination of downward continuation and local approximation for harmonic potentials
• Classical Fourier Analysis
• Interpolation and scattered data fitting on manifolds using projected Powell-Sabin splines
• On the use of symmetry in FFT computation
• An SVD in Spherical Surface Wave Tomography
• Fourth-Order Time-Stepping For Stiff PDEs On The Sphere
• A Pseudospectral Approach for Polar and Spherical Geometries
• Two-Dimensional Fourier Continuation and Applications
• Computing with Functions in the Ball
• Computing with Functions in Spherical and Polar Geometries II. The Disk
• Computing with Functions in Spherical and Polar Geometries I. The Sphere
• Fast Poisson solvers for spectral methods
• Application of double Fourier series to the shallow water equations on a sphere

This page was built for publication: A double Fourier sphere method for \(d\)-dimensional manifolds