Behavior of the Fourier–Walsh coefficients of a corrected function


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Abstract

We prove that, given a sequence {ak}k=1 with ak ↓ 0 and {ak}k=1l2, reals 0 < ε < 1 and p ∈ [1, 2], and fLp(0, 1), we can find fLp(0, 1) with mes{f ≠ f < ε whose nonzero Fourier–Walsh coefficients ck(f) are such that |ck(f)| = ak for k ∈ spec(f).

About the authors

L. N. Galoyan

Yerevan State University

Author for correspondence.
Email: levongaloyan@mail.ysu.am
Armenia, Yerevan

R. G. Melikbekyan

Yerevan State University

Email: levongaloyan@mail.ysu.am
Armenia, Yerevan

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