## Real Analysis Exchange

### OntheFourier-Walsh Coefficients

Martin G. Grigoryan

#### Abstract

For any $0<\epsilon <1,\ p\geq 1$ and each function $f\in L^{p}[0,1]$ one can find a function $g\in L^{p}[0,1],\ mes\{x\in \lbrack 0,1] ;\ g\neq f\}<\epsilon$, such that the sequence $\{|c_{k}(g)|,\ k\in spec(g)\}$ is monotonically decreasing, where $\{c_{k}(g)\}$ is\ the sequence of Fourier-Walsh coefficients of the function $g(x)$.

#### Article information

Source
Real Anal. Exchange, Volume 35, Number 1 (2009), 157-166.

Dates
First available in Project Euclid: 27 April 2010

https://projecteuclid.org/euclid.rae/1272376229

Mathematical Reviews number (MathSciNet)
MR2657293

#### Citation

Grigoryan, Martin G. OntheFourier-Walsh Coefficients. Real Anal. Exchange 35 (2009), no. 1, 157--166. https://projecteuclid.org/euclid.rae/1272376229

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