Representation of Measurable Functions by Series in Walsh Subsystems

For any sequence {omega(n)}(n is an element of N) tending to infinity we construct a "quasiquadratic" representation spectrum Lambda = {n(2) + o(omega(n))}(n is an element of N): for any almost everywhere (a. e.) finite measurable function f(x) there exists a series in the form Sigma(k is an element of N) a(k)w(k)(x) that converges a. e. to this function, where {w(k)(x)}(k is an element of N) is the Walsh system. We find representation spectra in the form {n(l) + o(n(l))}(n is an element of N), where l is an element of{2(k)}(k is an element of N).