Abstract We prove stronger variants of a multiplier theorem Kislyakov. The key ingredients are based on ideas Kislyakov and the Kahane–Salem–Zygmund inequality. As by-product, we show various theorems for spaces trigonometric polynomials n -dimensional torus $\mathbb {T}^n$ or Boolean cubes $\{-1,1\}^N$ . Our more abstract approach local Banach space theory has advantage that it allows to consi...

In this paper we study ultraflat sequences (Pn) of unimodular polynomials Pn ∈ Kn in general, not necessarily those produced by Kahane in his paper [Ka]. We examine how far is a sequence (Pn) of unimodular polynomials Pn ∈ Kn from being conjugate reciprocal. Our main results include the following. Theorem. Given a sequence (εn) of positive numbers tending to 0, assume that (Pn) is a (εn)-ultraf...

The goal is to extend Gleason’s notion of a frame function, which essential in his fundamental theorem quantum measurement, more general function acting on 1-tight, so-called, Parseval frames. We refer these functions as Gleason for reason our generalization that positive operator-valued measures (POVMs) are essentially equivalent frames and POVMs arise naturally measurement theory. prove under...

We prove a Kahane-Khinchin type result with a few random vectors, which are distributed independently with respect to an arbitrary log-concave probability measure on Rn. This is an application of small ball estimate and Chernoff’s method, that has been recently used in the context of Asymptotic Geometric Analysis in [1], [2].

As described in [7], self-dual codes are an important class of linear codes for both theoretical and practical reasons. It is a fundamental problem to classify self-dual codes of modest length and determine the largest minimum weight among self-dual codes of that length (see [7]). By the Gleason–Pierce theorem, there are nontrivial divisible self-dual codes over Fq for q = 2, 3 and 4 only, wher...