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Francis K. A. Allotey (Saltpond, Ghana 9 August 1932 – Accra, Ghana 2 November 2017) Read chapter Read first chapter

2019 | OriginalPaper | Chapter

Convergence of Fourier-Walsh Double Series in Weighted \(L_{\mu }^{p}[0,1)^{2}\)

Authors : Martin G. Grigoryan, Tigran M. Grigoryan, L. S. Simonyan

Published in: Analysis and Partial Differential Equations: Perspectives from Developing Countries

Publisher: Springer International Publishing

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Abstract

In this work we discuss the behavior of Fourier coefficients with respect to the Walsh double system, as well as \(L_{\mu }^{p}[0,1)^{2}\)-convergence of the spherical partial sums of the double Fourier-Walsh series after modification of functions.

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previous chapter Semiclassical Analysis of Dispersion Phenomena
next chapter “Strong” Turing-Hopf Instability for Reaction-Diffusion Systems
Literature
1.
2.
D’yachenko, M.I.: Some problems in the theory of multiple trigonometric series. Uspekhi Mat. Nauk 47(5) (16992), 97–162 (1992) (English transl. In Russian Math. Surveys 47)MathSciNetCrossRef
3.
4.
5.
Galoyan, L.N., Grigoryan, M.G., Kobelyan, AKh: Convergence of Fourier series in classical systems. Mat. Sb. 206(7), 55–94 (2015)MathSciNetCrossRef
6.
Getsadze, R.D.: On divergence in measure of general multiple orthogonal Furier series. Dokl. Akad. Nauk SSSR 306, 24–25 (1989) (English transl. in Soviet Math. Dokl. 39 1989)
7.
Golubov, B.I., Efimov, A.F., Skvortsov, V.A.: Series and Transformations of Walsh. Moskow (1987) (in Russian)
8.
Golubov, B.I.: Multiple Furier series and integrals. Itogi Nauki i Tekhniki Ser. Mat. Anal. 47(5), 97–162 (1992) (English transl. in J. Soviet Math. 24 1984)
9.
10.
Grigorian, M.G.: On the \(L^{p}\)-strong property of orthonormal systems. Math. sb. 194(10), 77–106 (2012) (in Russ., English transl. Sbornik: Math. 194(10), 1503–1532)
11.
Grigorian, M.G., Sargsyan, A.A.: On the coefficients of expansion of elements from C[0,1] space by the Faber-Schauder system. J. Funct. Spaces Appl. 2, 34–42 (2011)MathSciNet
12.
Grigorian, M.G., Zink, R.E.: Greedy approximation with respect to certain subsystems of the Walsh orthonormal system. Proc. Am. Math. Soc. 134(12), 3495–3505 (2006)MathSciNetCrossRef
13.
Grigoryan, M.G.: Modifications of functions, Fourier coefficients and nonlinear approximation. Mat. Sb. 203(3), 49–78 (2012)MathSciNetCrossRef
14.
Grigoryan, M.G.: Uniform convergence of the greedy algorithm with respect to the Walsh system. Studia Math. 198(2), 197–206 (2010)MathSciNetCrossRef
15.
Grigoryan, M.G., Gogyan, S.L.: On nonlinear approximation with respect to the Haar system and modifications of functions. An. Math. 32, 49–80 (2006)CrossRef
16.
Grigoryan, M.G., Krotov, V.G.: Luzin’s correction theorem and the coefficients of Fourier expansions in the faber-schauder system. Mat. Zametki 93(2), 172–178 (2013)MathSciNetCrossRef
17.
Grigoryan, M.G., Navasardyan, K.A.: On behavior of Fourier coefficients by Walsh systems. J. Contemp. Math. Anal. (Armen. Acad. Sci.) 51(1), 1–13 (2016)CrossRef
18.
Grigoryan, M.G.: On some properties of orthogonal systems. Izv. Ross. Akad. Nauk, Ser. Mat. 57(5), 75–105 (1993)
19.
Grigoryan, M.G., Sargsyan, A.A.: On the universal functions fr the class Lp[0,1]. J. Funct. Anal. 270, 3111–3133 (2016)MathSciNetCrossRef
20.
21.
Grigoryan, M.G.: Series in the classical systems. LAP LAMBERT Academic Publishing, Saarbruken (2017) (in Russian)
22.
23.
Kolmogorov, A.H.: Sur les fonctions harmoniques conjugees et les series. de Fourier, FM 7, 23–28 (1925)
24.
Luzin, N.N.: On the fundamental theorem of the integral calculus. Mat. Sb. 28, 266–294 (1912). (in Russian)
25.
Men’shov, D.E.: Sur la convergence uniforme des series de Fourier. Mat. Sb. 11(53), 67–96 (1942) (French; Russian)
26.
Men’shov, D.E.: On Fourier series of integrable functions. Trudy Moskov. Mat. Obshch. 1, 5–38 (1952)
27.
Paley, R.E.A.C.: A remarkable set of orthogonal functions. Proc. Lond. Math. Soc. 34, 241–279 (1932)CrossRef
28.
Riss, M.: Sur les fonctions conjugees. Math. Zeit. 27, 214–244 (1927)
29.
30.
Zhizhiashvili, L.V.: Some problems in the theory of simple and multiple trigonometric and orthogonal series. Uspekhi Mat. Nauk 28(2), 65–119 (1973) (English transl. In Russian, Math. Surveys 28 1973)CrossRef
Metadata
Title
Convergence of Fourier-Walsh Double Series in Weighted
Authors
Martin G. Grigoryan
Tigran M. Grigoryan
L. S. Simonyan
Copyright Year
2019
Book
Analysis and Partial Differential Equations: Perspectives from Developing Countries

Print ISBN: 978-3-030-05656-8

Electronic ISBN: 978-3-030-05657-5

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-05657-5_8

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