Abstract
In this paper we establish a number of theorems providing complete characterizations of divergence sets of general series in orthogonal bases with a localization property.
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References
H. Hahn, “Über die Menge der Konvergenzpunkte einer Funktionenfolge”, Arch. d. Math. u. Phys., 28, 34–45, 1919.
G. A. Karagulyan, “A complete characterization of divergence sets of Fourier-Haar series”, Journal of Contemporary Math. Analysis (Armenian Academy of Sciences), 45(6), 336–349, 2010.
G. A. Karagulyan, “Divergence of general localized operators on the sets of measure zero”, Colloq. Math., 121(1) 113–119, 2010.
G. A. Karagulyan, “On characterization of divergence sets of sequences of operators with localization property”, Mat. Sbornik, 202(1) 11–36, 2011.
B. S. Kashin, A. A. Sahakyan, Orthogonal Series (Nauka, Moscow, 1984).
M. A. Lunina, “On unbounded divergence sets of series by Haar system”, Vestn. Mosk. un-ta. Seriya 1, Mat. mech., 4, 13–20, 1976.
W. Sierpinski, “Sur Tensemble des points de convergence d’une suite de fonctions continues”, Fund. Math., 2, 41–49, 1921.
N. K. Bari, Trigonometric Series (Fizmatgiz, Moscow, 1961).
K. Zeller, “Über Konvergenzmengen von Fourierreihen”, Arch. Math., 2, 335–340, 1955.
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Original Russian Text © D. A. Karagulyan, 2012, published in Izvestiya NAN Armenii. Matematika, 2012, No. 5, pp. 39–48.
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Karagulyan, D.A. On unbounded divergence sets of series in orthonormal bases. J. Contemp. Mathemat. Anal. 47, 234–239 (2012). https://doi.org/10.3103/S1068362312050032
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DOI: https://doi.org/10.3103/S1068362312050032