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This article is cited in 4 scientific papers (total in 4 papers)
Uniqueness for multiple Haar series
M. G. Plotnikov Vologda State Academy of Milk Industry
Abstract:
Uniqueness questions are considered for multiple Haar series convergent over rectangles or in the sense of $\rho$-regular convergence. A condition is found ensuring that a given set is a relative uniqueness set under assumptions that are many-dimensional analogues of the Arutyunyan–Talalyan condition. This generalizes to $\rho$-regular convergence results for convergence over rectangles obtained by Movsisyan and Skvortsov. A monotonicity theorem is proved under very general assumptions for a dyadic-interval function used in the construction of a many-dimensional generalized integral of Perron type, which is called the $(P^{\rho,*}_d )$-integral. With the help of this integral one can recover by Fourier's formulae the coefficients of multiple Haar series from a fairly broad class including, in particular, series with power growth of partial sums at points with at least one dyadic rational coordinate. It is observed that already in the two-dimensional case the main results are best possible in a certain sense.
Received: 04.11.2003 and 30.08.2004
Citation:
M. G. Plotnikov, “Uniqueness for multiple Haar series”, Mat. Sb., 196:2 (2005), 97–116; Sb. Math., 196:2 (2005), 243–261
Linking options:
https://www.mathnet.ru/eng/sm1268https://doi.org/10.1070/SM2005v196n02ABEH000879 https://www.mathnet.ru/eng/sm/v196/i2/p97
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Abstract page: | 472 | Russian version PDF: | 210 | English version PDF: | 12 | References: | 68 | First page: | 1 |
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