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Note on Decreasing Rearrangement of Fourier Series
-
S. Kostyukovsky
Published/Copyright:
June 4, 2010
Abstract
In this note we construct a complete orthonormal system (ONS) of uniformly bounded functions, such that for any function ƒ ∈ L2[0,1] its Fourier series with respect to the system, taken in decreasing order of magnitude of the coefficients, converges almost everywhere.
Received: 1997-01-23
Revised: 1997-04-09
Published Online: 2010-06-04
Published in Print: 1997-June
©Heldermann Verlag
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- Note on Decreasing Rearrangement of Fourier Series
Keywords for this article
Fourier expansions;
complete orthonormal systems;
decreasing rearrangement
Articles in the same Issue
- Optimal Synthesis for Nonoscillatory Controlled Objects
- Forced Oscillations of First Order Nonlinear Neutral Differential Equations
- Continuity of the Superposition of Set–Valued Functions
- On the Uniqueness of Lebesgue and Borel Measures
- Optimality Conditions for Control Problems Governed by Abstract Semilinear Differential Equations in Complex Banach Spaces
- On the Continuity of Random Operators
- Norms on Possibilities II: More CCC Ideals on 2ω
- Stationary Solutions for Heat Equation Perturbed by General Additive Noise
- Note on Decreasing Rearrangement of Fourier Series
