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Fourier analysis on trapezoids with curved sides

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  • Zhihua Zhang

    (Beijing Normal University)

Abstract

It is well known that smooth periodic functions can be expanded into Fourier series and can be approximated by trigonometric polynomials. The purpose of this paper is to do Fourier analysis for smooth functions on planar domains. A planar domain can often be divided into some trapezoids with curved sides, so first we do the Fourier analysis for smooth functions on trapezoids with curved sides. We will show that any smooth function on a trapezoid with curved sides can be expanded into Fourier sine series with simple polynomial factors, and so it can be well approximated by a combination of sine polynomials and simple polynomials. Then we consider the Fourier analysis on the global domain. Finally, we extend these results to the three-dimensional case.

Suggested Citation

  • Zhihua Zhang, 2012. "Fourier analysis on trapezoids with curved sides," Indian Journal of Pure and Applied Mathematics, Springer, vol. 43(5), pages 495-520, October.
    • Handle: RePEc:spr:indpam:v:43:y:2012:i:5:d:10.1007_s13226-012-0030-3
    DOI: 10.1007/s13226-012-0030-3
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