Some Notes on Flat Polynomials

Abstract

Connection of flat polynomials with some spectral questions in ergodic theory is discussed. A necessary condition for a sequence of polynomials of the type $\frac{1}{\sqrt{N}}(1+{\sum }_{j=1}^{N-1}{z}^{n_j})$ to be flat in almost everywhere sense is given, which contrasts with a similar necessary condition for a sequence of polynomials to be ultraflat.

13 pages

References in corpus (1)

• A non-singular transformation whose spectrum has Lebesgue component of multiplicity one

Cited by in corpus (3)

• On flat polynomials with non-Negative coefficients
• On the spectral type of rank one flows and Banach problem with calculus of generalized Riesz products on the real line
• On the Mahler measure of the spectrum of rank one maps