Journal of Applied Analysis EMIS ELibM Electronic Journals Journal of Applied Analysis
Vol. 3, No. 1, pp. 137-142 (2003)

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Note on decreasing rearrangement of Fourier

S.Kostyukovsky and A.Olevskii

School of Mathematical Sciences
Sackler Faculty of Exact Sciences
Tel Aviv University
Ramat Aviv 69978

Abstract: In this note we construct a complete orthonormal system (ONS) of uniformly bounded functions, such that for any function $f\in L^2[0,1]$ its Fourier series with respect to the system, taken in decreasing order of magnitude of the coefficients, converges almost everywhere.

Keywords: Fourier expansions, complete orthonormal systems, decreasing rearrangement

Classification (MSC2000): 42C15, 42C20

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Electronic version published on: 12 Jun 2003. This page was last modified: 12 Jun 2003.

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