Abstract
We prove that, given a sequence {ak}k=1 ∞ with a k ↓ 0 and {ak}k=1 ∞ ∉ l 2, reals 0 < ε < 1 and p ∈ [1, 2], and f ∈ L p(0, 1), we can find f ∈ L p(0, 1) with mes{f ≠ f < ε whose nonzero Fourier–Walsh coefficients c k (f) are such that |c k (f)| = a k for k ∈ spec(f).
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Yerevan. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 57, No. 3, pp. 641–649, May–June, 2016; DOI: 10.17377/smzh.2016.57.311.
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Galoyan, L.N., Melikbekyan, R.G. Behavior of the Fourier–Walsh coefficients of a corrected function. Sib Math J 57, 505–512 (2016). https://doi.org/10.1134/S0037446616030113
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DOI: https://doi.org/10.1134/S0037446616030113