2022/05/10 by Alexander Volberg, Volberg, Alexander
Mathematics · #Advanced Harmonic Analysis Research #Bounded function #Combinatorics #Computer science #Constant (computer programming) #Degree (music) #Discrete mathematics #Holomorphic and Operator Theory #Mathematical analysis #Mathematics #Orthogonal polynomials #Physics #Pure mathematics #Spectral Theory in Mathematical Physics #Type (biology) #Unimodular matrix #acm:06E30 #acm:47A30 #acm:81P45 #math.AP #msc:06E30 #msc:47A30 #msc:81P45
paper · pdf · doi:10.48550/arxiv.2205.04936
published in arXiv (Cornell University) (Cornell University) · 12 pages; the mistake was found in the previous version by A. Borichev. Corrected, but this makes the result much weaker
openalex publication_date 2022/05/10 · openalex created_date 2022/05/22 · arxiv created 2022/05/25 · arxiv updated 2022/05/27 · openalex updated_date 2026/08/06
In this paper we are concerned with the Bohnenblust--Hille type inequalities for certain polynomials of bounded degree but of very large number of variables. As the polynomials will be defined on groups, one can think about the problem as the estimate of Sidon constants. In most cases the sharp constants are unknown. We estimate the universal constant concerning the Sidon type estimates of degree d polynomials of n variables z1, …, zn with unimodular coefficients. For polynomials that have constant absolute value of coefficients, this allows us to improve the estimate from \citeDGMS. The main result is Theorem 1.7 below.