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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, Number 1, Pages 10–20
(Mi ivm9314)
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This article is cited in 2 scientific papers (total in 2 papers)
Generalized absolute convergence of series from Fourier coeficients by systems of Haar type
S. S. Volosivetsa, B. I. Golubovb a Saratov State University,
83 Astrakhanskya str., Saratov, 410012 Russia
b Moscow Institute of Physical Technologies (State University),
9 Institutskii Lane, Dolgoprudnyi, Moscow Region, 141700 Russia
Abstract:
For orthogonal systems of Haar type introduced by N.Ya. Vilenkin in 1958 we study absolute convergence of series from Fourier coefficients raised to a positive power with multiplicators from Gogoladze–Meskhia class. The conditions for convergence of the series mentioned above are given in terms of best approximations of functions in $L^p$ spaces by polynomials with respect to Haar type systems or in terms of fractional modulus of continuity of functions from Wiener spaces $V_p$, $p>1$. We establish the sharpness of obtained results.
Keywords:
Haar type system, Fourier coefficients, $L^p$ space, functions of bounded $p$-variation, best approximation, modulus of continuity.
Received: 26.08.2016
Citation:
S. S. Volosivets, B. I. Golubov, “Generalized absolute convergence of series from Fourier coeficients by systems of Haar type”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 1, 10–20; Russian Math. (Iz. VUZ), 62:1 (2018), 7–16
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https://www.mathnet.ru/eng/ivm9314 https://www.mathnet.ru/eng/ivm/y2018/i1/p10
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Abstract page: | 264 | Full-text PDF : | 48 | References: | 28 | First page: | 13 |
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