Abstract
We consider the question of existence of trigonometric series universal in weighted
Open AccessUniversal series by trigonometric system in weighted
Universal series by trigonometric system in weighted L μ 1
Received17 Apr 2006
Accepted09 Nov 2006
Published17 Dec 2006
References
F. G. Arutjunjan, “Representation of functions by multiple series,” Akademiya Nauk Armyanskoĭ SSR. Doklady, vol. 64, no. 2, pp. 72–76, 1977.
View at: Google Scholar | MathSciNetS. A. Episkoposian, “On the existence of universal series by trigonometric system,” Journal of Functional Analysis, vol. 230, no. 1, pp. 169–183, 2006.
View at: Google Scholar | MathSciNetM. G. Grigorian, “On the representation of functions by orthogonal series in weighted spaces,” Studia Mathematica, vol. 134, no. 3, pp. 207–216, 1999.
View at: Google Scholar | Zentralblatt MATH | MathSciNetM. G. Grigorian and S. A. Episkoposian, “Representation of functions in the weighted space by trigonometric and Walsh series,” Analysis Mathematica, vol. 27, no. 4, pp. 261–277, 2001.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetV. Ya. Kozlov, “On complete systems of orthogonal functions,” Matematicheskiĭ Sbornik, vol. 26(68), pp. 351–364, 1950.
View at: Google Scholar | MathSciNetD. E. Menshov, “On the partial summs of trigonometric series,” Matematicheskiĭ Sbornik, vol. 20, pp. 197–238, 1947.
View at: Google ScholarW. Orlicz, “Uber die unabhangig von der Anordnung fast uberall kniwergenten Reihen,” Bulletin de l'Académie Polonaise des Science, vol. 81, pp. 117–125, 1927.
View at: Google ScholarA. A. Talaljan, “On the convergence almost everywhere of subsequences of partial sums of general orthogonal series,” Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, vol. 10, no. 3, pp. 17–34, 1957.
View at: Google Scholar | MathSciNetA. A. Talaljan, “Series universal with respect to rearrangement,” Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, vol. 24, pp. 567–604, 1960.
View at: Google Scholar | MathSciNetP. L. Ul'yanov, “Unconditional convergence and summability,” Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, vol. 22, pp. 811–840, 1958.
View at: Google Scholar | MathSciNet
Copyright
Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.