Abstract
For any sequence {ω(n)} n∈ℕ tending to infinity we construct a “quasiquadratic” representation spectrum Λ = {n 2 + o(ω(n))} n∈ℕ: for any almost everywhere (a. e.) finite measurable function f(x) there exists a series in the form \( \mathop \sum \limits_{k \in \Lambda } \) α k ω k (x) that converges a. e. to this function, where {w k (x)} k∈ℕ is the Walsh system. We find representation spectra in the form {n l + o(n l)} n∈ℕ, where l ∈ {2k} k∈ℕ.
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Original Russian Text © M.A. Nalbandyan, 2009, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, No. 10, pp. 51–62.
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Nalbandyan, M.A. Representation of measurable functions by series in Walsh subsystems. Russ Math. 53, 45–56 (2009). https://doi.org/10.3103/S1066369X09100065
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DOI: https://doi.org/10.3103/S1066369X09100065