61 citations · 128 across the 20 of their papers we have counts for
11 papers · 1 filter
One cannot hear the winding number
Jean Bourgain, Gady Kozma
We construct an example of two continuous maps f and g of the circle to itself with the same absolute value of the Fourier transform but with different winding numbers, answering a…
On the gaps between zeros of trigonometric polynomials
Gady Kozma, Ferenc Oravecz
We show that for every finite symetric set S of integer vectors, every real trigonometric polynomial on the d dimensional torus with spectrum in S has a zero in every closed ball o…
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…