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Ferenc Moricz - One of the best experts on this subject based on the ideXlab platform.
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absolute convergence of multiple Fourier Series revisited
Analysis Mathematica, 2008Co-Authors: Ferenc Moricz, Antal VeresAbstract:In a recent paper [4], Gogoladze and Meskhia generalized the classical results of Bernstein, Szasz, Zygmund and others related to absolute convergence of single trigonometric Fourier Series. Our aim is to extend these results from single to multiple Fourier Series. To this effect, we introduce the notions of multiplicative moduli of continuity and that of smoothness. Multiplicative Lipschitz classes of functions in several variables, and functions of bounded s-variation in the sense of Vitali are also considered.
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absolutely convergent Fourier Series and function classes
Journal of Mathematical Analysis and Applications, 2006Co-Authors: Ferenc MoriczAbstract:Abstract We study the smoothness property of a function f with absolutely convergent Fourier Series, and give best possible sufficient conditions in terms of its Fourier coefficients to ensure that f belongs either to one of the Lipschitz classes Lip ( α ) and lip ( α ) for some 0 α ⩽ 1 , or to one of the Zygmund classes Λ ∗ ( 1 ) and λ ∗ ( 1 ) . Our theorems generalize some of those by Boas [R.P. Boas Jr., Fourier Series with positive coefficients, J. Math. Anal. Appl. 17 (1967) 463–483] and one by Nemeth [J. Nemeth, Fourier Series with positive coefficients and generalized Lipschitz classes, Acta Sci. Math. (Szeged) 54 (1990) 291–304]. We also prove a localized version of a theorem by Paley [R.E.A.C. Paley, On Fourier Series with positive coefficients, J. London Math. Soc. 7 (1932) 205–208] on the existence and continuity of the derivative of f.
Ferenc Weisz - One of the best experts on this subject based on the ideXlab platform.
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Θ-summability of Fourier Series
Acta Mathematica Hungarica, 2004Co-Authors: Ferenc WeiszAbstract:A general summability method of orthogonal Series is given with the help of an integrable function Θ. Under some conditions on Θ we show that if the maximal Fejer operator is bounded from a Banach space X to Y, then the maximal Θ-operator is also bounded. As special cases the trigonometric Fourier, Walsh, Walsh--Kaczmarz, Vilenkin and Ciesielski--Fourier Series and the Fourier transforms are considered. It is proved that the maximal operator of the Θ-means of these Fourier Series is bounded from Hp to Lp (1/2
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θ summability of Fourier Series
Acta Mathematica Hungarica, 2004Co-Authors: Ferenc WeiszAbstract:A general summability method of orthogonal Series is given with the help of an integrable function Θ. Under some conditions on Θ we show that if the maximal Fejer operator is bounded from a Banach space X to Y, then the maximal Θ-operator is also bounded. As special cases the trigonometric Fourier, Walsh, Walsh--Kaczmarz, Vilenkin and Ciesielski--Fourier Series and the Fourier transforms are considered. It is proved that the maximal operator of the Θ-means of these Fourier Series is bounded from Hp to Lp (1/2
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Summability of D-Dimensional Walsh-Fourier Series
Summability of Multi-Dimensional Fourier Series and Hardy Spaces, 2002Co-Authors: Ferenc WeiszAbstract:In this chapter we consider the Cesaro and Riesz summability of multiparameter Walsh-Fourier Series. For summations of the trigonometric-Fourier Series see Chapter 5.
Mikhail Ivanovich Dyachenko - One of the best experts on this subject based on the ideXlab platform.
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On a class of summability methods for multiple Fourier Series
Sbornik: Mathematics, 2013Co-Authors: Mikhail Ivanovich DyachenkoAbstract:The paper shows that the same properties which hold for the classical -means are preserved for a sufficiently large class of summability methods for multiple Fourier Series involving rectangular partial sums. More precisely, Fourier Series of continuous functions are uniformly summable by these methods, and Fourier Series of functions from the class are summable almost everywhere. Bibliography: 6 titles.
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$ u$-convergence of multiple Fourier Series
Izvestiya: Mathematics, 1995Co-Authors: Mikhail Ivanovich DyachenkoAbstract:The -convergence of multiple Fourier Series is studied, generalizing convergence in the Pringsheim sense, with respect to spheres. A definitive condition in terms of moduli of smoothness is found on a functional class that implies the -convergence of Fourier Series in the metrics , where , and .
Agamirza Bashirov - One of the best experts on this subject based on the ideXlab platform.
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Chapter 12 - Fourier Series and Integrals
Mathematical Analysis Fundamentals, 2014Co-Authors: Agamirza BashirovAbstract:Chapter 12 presents Fourier Series. Pointwise, uniform and mean square convergence of Fourier Series and conditions for them are discussed. Fourier Series in abstract inner product spaces is also considered. Cesaro summability and Fejer’s theorem are presented. Completeness of trigonometric functions, Gibb’s phenomenon are discussed. The chapter ends with introduction to Fourier integrals.
Jungsoo Rhee - One of the best experts on this subject based on the ideXlab platform.
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gibbs phenomenon and certain nonharmonic Fourier Series
Communications of The Korean Mathematical Society, 2011Co-Authors: Jungsoo RheeAbstract:The Fourier Series has a rapid oscillation near end points at jump discontinuity which is called the Gibbs phenomenon. There is an overshoot (or undershoot) of approximately 9% at jump discontinuity. In this paper, we prove that a bunch of Series representations (certain nonharmonic Fourier Series) give good approximations vanishing Gibbs phenomenon. Also we have an application for approximating some shape of upper part of a vehicle in a different way from the method of cubic splines and wavelets.