The General Orthogonal Expansions
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In this and the following two chapters, we shall depart from the typical Gibbs phenomenon in the trigonometric polynomials and the truncated Fourier integrals approximations of functions with jump discontinuities. We will cover similar Gibbs phenomenon in the truncated, orthogonal expansion, or general integral transforms representations of functions with jump discontinuities.
KeywordsFourier Series Jump Discontinuity Gibbs Phenomenon Orthogonal Expansion Spherical Average
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Additional References (From Appendix A.)
- A.2A.J. Jerri, The Gibbs phenomenon in sampling and interpolation in sampling and interpolation, The Proceedings of the 1997 International Workshop on Sampling Theory and its Applications, June 16–19, 1997, Aveiro, Portugal, pp. 1–9.Google Scholar
- A.76J.A. Letellier, Summing orthogonal polynomials to avoid Gibbs phenomenon. Ph.D. Thesis, University of Wisconsin-Milwaukee, 1992.Google Scholar