On flat trigonometric sums and ergodic flow with simple Lebesgue spectrum

Details On flat trigonometric sums and ergodic flow with simple Lebesgue spectrum On flat trigonometric sums and ergodic flow with simple Lebesgue spectrum

2010-02-15

arxiv.org/abs/1002.2808v1

Mathematics

Dynamical Systems

19 pages; 2 figures

Scientific paper

A complex polynomial $P(z) = c_0 + c_1 z +...+ c_n z^n$ is called unimodular if $|c_j| = 1$, $j = 0,...,n$. Littlewood asked the question (1966) on how close a unimodular polynomial come to satisfying $|P(z)| \approx \sqrt{n+1}$ if $n \ge 1$? In this paper we show that for a given $0 < a < b$ and $\eps > 0$ there exist trigonometric sums $\cP(t) = n^{-1/2} \sum_{j=0}^{n-1} \exp(2\pi i t\omega(j))$ with a real frequency function $\omega(j)$ which are $\eps$-flat on segment $[a,b]$ acording to the norm in $L^1([a,b])$ (as well as in $L^2([a,b])$). We apply this method to construct a dynamical system having simple spectrum and Lebesgue spectral type in the class of rank-one flows.

Affiliated with

Also associated with

No associations

Rating

On flat trigonometric sums and ergodic flow with simple Lebesgue spectrum does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On flat trigonometric sums and ergodic flow with simple Lebesgue spectrum, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On flat trigonometric sums and ergodic flow with simple Lebesgue spectrum will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-145726