Use of Fourier series in S2 to approximate star-shaped surfaces

Authors

  • Miguel Nasarre Budiño Universitat Autònoma de Barcelona

Keywords:

Laplacian, Riemannian manifold, basis, spherical harmonics, Fourier series, L2-error estimates

Abstract

First we will focus in extending the notion of Fourier series, studying how can we represent functions of integrable square over Riemannian manifolds. To do this we will use the Hodge theorem, that will allow us to find basis of these spaces through the Laplacian. Then we will see how this method can be used to find the Fourier series for periodic functions, and for the functions L2(S2), our main case of study. We will also discuss how to estimate the L2-error, and we implement all the formulas found in the article in a program to be able to visualize the obtained results.

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Published

2025-12-04

How to Cite

Nasarre Budiño, M. (2025). Use of Fourier series in S<sup>2</sup> to approximate star-shaped surfaces. Reports@SCM, 10(1), 63–74. Retrieved from https://revistes.iec.cat/index.php/reports/article/view/155423

Issue

Vol. 10 No. 1 (2025)

Section

Articles

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