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Mathematical Notes, 2016
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Bloshanskii, I. L., Grafov, D. A.
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Bloshanskii, I. L., Grafov, D. A.
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Mining Multiple Periodic Time Series for Detecting Unusual Sub-Sequences
2009 Fourth International Conference on Innovative Computing, Information and Control (ICICIC), 2009Advances 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
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Mathematical Notes, 2014
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Bloshanskii, I. L., Tsukareva, Z. N.
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Bloshanskii, I. L., Tsukareva, Z. N.
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ON THE COMMUTATIVITY OF MULTIPLE SERIES AND BASIC SEQUENCE
Acta Mathematica Scientia, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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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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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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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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Proceedings of the Steklov Institute of Mathematics, 2014
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Bloshanskaya, S. K., Bloshanskii, I. L.
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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, 1995In 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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