43 citations · 122 across the 29 of their papers we have counts for
7 papers · 1 filter
Representation of non periodic functions by trigonometric series with almost integer frequencies
Gady Kozma, Alexander Olevskii
Inspired by Menshov's representation theorem, we prove that there exists a sequence of frequecies such that any measurable (complex valued) function on R can be represented as a su…
An "Analytic" Version of Menshov's Representation Theorem
Gady Kozma, Alexander Olevskii
Every measurable function f on the circle can be represented as a sum of harmonics with positive spectrum, converging in measure. For convergence almost everywhere this is not true…
Menshov representation spectra
Gady Kozma, Alexander Olevskii
A Menshov spectrum is a subset of the integers that is sufficient for representing every measurable function as an almost-everywhere converging trigonometric (non-Fourier) sum. In…
Random Menshov spectra
Gady Kozma, Alexander Olevskii
We show that a spectrum of frequencies obtained by a random perturbation of the integers allows one to represent any measurable function on R by an almost everywhere converging sum…
A null series with small anti-analytic part
Gady Kozma, Alexander Olevskii
We show that it is possible for a square integrable function on the circle, which is a sum of an almost everywhere convergent series of exponentials with positive frequencies, to n…
Maximal smoothness of the anti-analytic part of a trigonometric null series
Gady Kozma, Alexander Olevskii
We proved recently math.CA/0510403 that the anti-analytic part of a trigonometric series, converging to zero almost everywhere, may be square integrable on the circle. Here we prov…