Abstract
Some well-known properties of the trigonometric system as well as of the Haar and Welsh systems are generalized to general orthonormal systems.

Editor-in-Chief: Kiguradze, Ivan / Shervashidze, T.
Editorial Board Member: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, J. / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio
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1Faculty of Mechanics and Mathematics, I. Javakhishvili Tbilisi State University, 2, University St., Tbilisi 0143, Georgia
Citation Information: Georgian Mathematical Journal. Volume 10, Issue 2, Pages 363–379, ISSN (Online) 1072-9176, ISSN (Print) 1072-947X, DOI: 10.1515/GMJ.2003.363, March 2010
Some well-known properties of the trigonometric system as well as of the Haar and Welsh systems are generalized to general orthonormal systems.
Key words and phrases:: Orthonormal system; Fourier coefficients; modulus of continuity; bounded variation
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