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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, Number 1, Pages 67–71
(Mi ivm8421)
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This article is cited in 3 scientific papers (total in 3 papers)
Coefficients of convergent multiple Haar series
M. G. Plotnikov Chair of Higher Mathematics and Physics, The Vereshchagin Vologda State Dairy Farming Academy, Molochnoye, Vologda, Russia
Abstract:
It is well-known that if a multiple trigonometric series almost everywhere converges in the square or restricted rectangular sense to a finite function, then its coefficients grow slower than any exponential function. In this paper we prove the existence of a multiple Haar series that converges in the square or restricted rectangular sense to a finite function and contains a subsequence of coefficients that grows faster than any sequence defined an advance. Moreover, we show that for such series conditions of the Arutyunyan–Talalyan type can be violated at some points.
Keywords:
Haar system, multiple Haar series, convergence in the square sense, convergence in the restricted rectangular sense, Cantor–Lebesgue type theorems.
Received: 20.12.2010
Citation:
M. G. Plotnikov, “Coefficients of convergent multiple Haar series”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 1, 67–71; Russian Math. (Iz. VUZ), 56:1 (2012), 61–65
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https://www.mathnet.ru/eng/ivm8421 https://www.mathnet.ru/eng/ivm/y2012/i1/p67
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Abstract page: | 318 | Full-text PDF : | 73 | References: | 66 | First page: | 6 |
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