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De Michele, L.; Di Natale, M.; Roux, D.

Fejér kernels and noisy Fourier series. (English) Zbl 0794.65097

J. Comput. Appl. Math. 49, No. 1-3, 45-50 (1993).
This paper is continuing the authors’ work in inverse Fourier transform of noisy series. They give some estimates for implementation of a general method of noisy Fourier transform in the case of Fejér means.
Reviewer: M.Gaşpar (Iaşi)

MSC:

65T40 Numerical methods for trigonometric approximation and interpolation
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series

Keywords:

Fejér kernels; noisy Fourier series; inversion method; error estimates; inverse Fourier transform; noisy Fourier transform; Fejér means
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References:

[1] Bokhner, S., Lectures on Fourier Integrals (1962), Nauka: Nauka Moscow · Zbl 0103.32701
[2] De Michele, L.; Di Natale, M.; Roux, D., Inverse Fourier transform, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 1, 9, 305-308 (1990) · Zbl 0711.42014
[3] De Michele, L.; Di Natale, M.; Roux, D., Sharp properties of a regularization method for inversion of Fourier series, Atti Sem. Mat. Fis. Univ. Modena, 39, 253-267 (1991)
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[5] De Michele, L.; Di Natale, M.; Roux, D., On the effectiveness of some inversion methods for noisy Fourier series, (Singh, S. P., Approximation Theory, Spline Functions and Applications, 356 (1992), Kluwer: Kluwer Dordrecht), 255-267, NATO Adv. Sci. Inst. · Zbl 0745.42001
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