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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, Number 10, Pages 51–62
(Mi ivm3077)
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This article is cited in 1 scientific paper (total in 1 paper)
Representation of measurable functions by series with respect to Walsh subsystems
M. A. Nalbandyan Chair of Higher Mathematics, Erevan State University, Erevan, Republic of Armenia
Abstract:
For every sequence $\{\omega(n)\}_{n\in\mathbb N}$ that tends to infinity we construct a “quasiquadratic” representation spectrum $\Lambda=\{n^2+o(\omega(n))\}_{n\in\mathbb N}$: for each almost everywhere finite measurable function $f(x)$ there exists a series in the form $\sum_{k\in\Lambda}a_kw_k(x)$ that converges almost everywhere to this function, where $\{w_k(x)\}_{k\in\mathbb N}$ is the Walsh system.
We also find representation spectra in the form $\{n^l+o(n^l)\}_{n\in\mathbb N}$, where $l\in\{2^k\}_{k\in\mathbb N}$.
Keywords:
Walsh system, orthogonal series, representation theorems, expansion spectrum.
Received: 13.06.2007
Citation:
M. A. Nalbandyan, “Representation of measurable functions by series with respect to Walsh subsystems”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, no. 10, 51–62; Russian Math. (Iz. VUZ), 53:10 (2009), 45–56
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https://www.mathnet.ru/eng/ivm3077 https://www.mathnet.ru/eng/ivm/y2009/i10/p51
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Abstract page: | 268 | Full-text PDF : | 62 | References: | 44 | First page: | 3 |
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