Abstract
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.
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Additional References (From Appendix A.)
A.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.
J.A. Letellier, Summing orthogonal polynomials to avoid Gibbs phenomenon. Ph.D. Thesis, University of Wisconsin-Milwaukee, 1992.
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© 1998 Springer Science+Business Media Dordrecht
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Jerri, A.J. (1998). The General Orthogonal Expansions. In: The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations. Mathematics and Its Applications, vol 446. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2847-7_3
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DOI: https://doi.org/10.1007/978-1-4757-2847-7_3
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