Year: 2026
Type: preprint
Abstract: The goal of this paper is to prove an upper bound for the $L^4$ norm of a trigonometric polynomial whose spectrum is a nontrivial strictly monotone polynomial with integer coefficients of degree three and higher, via its $L^2$ norm. Our condition on the coefficients of the trigonometric polynomial in question is that they form a complex sequence whose modulus is decreasing. Second, we obtain a similar result in the case where the spectrum is formed by perfect squares, under a more strict condition on the coefficients. Our results strengthen and complement those by S. Bochkarev and A. Córdoba. We also give an answer to a conjecture of Eceizabarrena and Da Rocha and determine the sharp order of growth of the $L^4$ norm of the trigonometric polynomial in this conjecture.
Source: arXiv (Cornell University)
Author: Vasilyev, Ioann
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G6444257319
OpenAlex ID: W7203865176