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Equiconvergence of expansions in multiple Fourier series and in fourier integrals with “lacunary sequences of partial sums”

Mathematical Notes, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bloshanskii, I. L., Grafov, D. A.
exaly   +2 more sources

Mining Multiple Periodic Time Series for Detecting Unusual Sub-Sequences

2009 Fourth International Conference on Innovative Computing, Information and Control (ICICIC), 2009
Advances in computer and information technology have opened a new avenue in the analysis of large and more detailed datasets that has become possible to observe. Most of the classical methodologies and techniques have become obsolete and fresh approaches of data analysis are overdue.
Jamal Ameen, Rawshan Basha
exaly   +2 more sources

Rudiments of multiple sequences and series

Alberto Debernardi Pinos   +2 more
exaly   +2 more sources

Localization for multiple Fourier series with “J k -lacunary sequence of partial sums” in Orlicz classes

Mathematical Notes, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bloshanskii, I. L., Tsukareva, Z. N.
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ON THE COMMUTATIVITY OF MULTIPLE SERIES AND BASIC SEQUENCE

Acta Mathematica Scientia, 2003
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Maximal sets of convergence and unbounded divergence of multiple fourier series with J κ -lacunary sequence of partial sums

Mathematical Notes, 2009
The authors characterize the structure and geometry of maximal sets of unbounded divergence and maximal sets of convergence almost everywhere of multiple Fourier series with a \(J_{k}\)-lacunary sequence of rectangular partial sums \(S_{n^{\left( \alpha \right) }\left[ J_{k}\right] }\left( x;f\right) \) for functions \(f\in L_{p}\left( T^{N}\right)\), \
Bloshanskii, I. L., Lifantseva, O. V.
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Equiconvergence of expansions in multiple trigonometric Fourier series and integrals in the case of a lacunary sequence of partial sums

Doklady Mathematics, 2013
296 We investigate the equiconvergence onN = (-π, π) N of expansions in multiple trigonometric Fourier series and Fourier integrals of functions f ∈ Lp( N ) and g ∈ L p ( N ), p > 1, N ≥ 2, g(x )= f (x) onN , in the case when the "partial sums" of these expansions, i.e., Sn(x; f ) and Jα(x; g), respectively, have "indices" n =( n1, n2, …, nN) ∈ N ...
I. L. Bloshanskii, D. A. Grafov
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A weak generalized localization criterion for multiple Walsh-Fourier series with J k -lacunary sequence of rectangular partial sums

Proceedings of the Steklov Institute of Mathematics, 2014
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Bloshanskaya, S. K., Bloshanskii, I. L.
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THE TENSOR BMO-PROPERTY OF THE SEQUENCE OF PARTIAL SUMS OF A MULTIPLE FOURIER SERIES

Russian Academy of Sciences. Sbornik Mathematics, 1995
In order to shorten notations, we present the results in the two- dimensional case. Denote by \(S_k(f, x)\) the rectangular partial sums of the double Fourier series of a function \(f\in L(T^2)\), \(k= (k_1, k_2)\), and \(x= (x_1, x_2)\). The author proved in Mat. Zametki 50, No. 1, 148-150 (1991; Zbl 0781.42013) that the operator \[ T_1 f(x):= \sup_{m\
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