Harmonic analysis for star graphs and the spherical coordinate trapezoidal rule

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摘要

Novel ideas in harmonic analysis are used to analyze the trapezoidal rule integration for two spheres. Sampling in spherical coordinates links three levels of harmonic analysis. Eigenfunctions of a nonstandard manifold Laplacian descend by restriction, first to a differential graph Laplacian, and then to difference operators. Trapezoidal rule integration with appropriate sampling is exact on eigenspaces of the manifold Laplacian, a fact which leads to trapezoidal rule error estimates on Sobolev-style spaces of functions. Singular functions with accurate trapezoidal rule integrals are identified, and a simplified analysis of smooth function numerical integration is provided.

论文关键词:65D30,65T99,34B45,Analysis on graphs,Harmonic analysis,Graph FFT,Product trapezoidal rule

论文评审过程:Received 27 February 2009, Revised 1 October 2010, Available online 20 October 2010.

论文官网地址:https://doi.org/10.1016/j.cam.2010.10.006