123 citations · 651 across the 93 of their papers we have counts for
8 papers · 2 filters
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…
Random homeomorphisms and Fourier expansions - the pointwise behavior
Gady Kozma
Let phi be a Dubins-Freedman random homeomorphism on [0,1] derived from the base measure uniform on the vertical line x=1/2, and let f be a periodic function satisfying that |f(x)-…
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…
Is PLA large?
Gady Kozma, Alexander Olevskii
We examine the class of functions representable by an analytic sum (by which we mean a trigonometric sum involving only positive frequencies) converging almost everywhere. We show…