RA Abstract. In his proof of Szemer ́edi’s Theorem, Gowers introduced certain norms that are defined on a parallelepip. d structure. A natural question is on which sets a parallelepiped …

Gowers norm (plural Gowers norms) (mathematics) In the field of additive combinatorics, a class of norms on functions on a finite group or group-like object which quantify the amount of …

Mar 17, 2024 · British mathematician most famous for connecting the fields of functional analysis and combinatorics. William Timothy Gowers was awarded a Fields Medal in 1998 1998 at the …

Gowers norms have been studied extensively both in the direct sense, starting with a function and understanding the associated norm, and in the inverse sense, starting with the norm and …

Aug 5, 2023 · The Gowers uniformity norm of h of k th order or U k norm of h, denoted by ‖ h ‖ U k, is defined as ‖ h ‖ U k = (E x, x 1, …, x k ∈ F 2 n [∏ S ⊆ [k] h (x ⊕ ∑ i ∈ S x i)]) 1 2 k, where …

Jun 17, 2017 · I think you want some complex conjugates in your definition of Gowers norm, although it won't affect the proofs of the last two properties, as you are working in F2 F 2. You …

Expand on how Gowers norm can be used as a metric for the "randomness" of a set of numbers

The Gowers U2 norm of a function is a measure of its resistance to a ne approximation. Although nonlinearity serves the same purpose for the classical Boolean functions, it does not extend …

In mathematics, in the field of additive combinatorics, a Gowers norm or uniformity norm is a class of norms on functions on a finite group or group-like object which quantify the amount of …

Mar 26, 2011 · The inverse conjecture for the Gowers norms, rst formulated precisely in [19, x8], postulates that this class of functions (which contains the polynomial phases) represents the …

R 0 by a weighted hypergraph in the proof of the relative Szemeredi theorem [1, x3] preserves the Gowers uniformity norm. The following inequality is the Gowers-Cauchy-Schwarz inequality for …

May 23, 2013 · In that paper, we showed how to prove a relative Szemerédi theorem for (r+1) -term arithmetic progressions assuming a linear forms condition. Here we show how to replace …

We prove the so-called inverse conjecture for the Gowers Us+1-norm in the case s = 3 (the cases s < 3 being established in previous literature). That is, we show that if f : [N] → ℂ is a function …

In his seminal work on Szemeredi's Theorem, Gowers [2] introduced uni-formity norms U(d) for each integer d 1, now referred to as Gowers norms or Gowers uniformity norms, that have …

In Chapter 2, we describe the background on Fourier analysis and the Gowers norm that we need to obtain our results, and we also give an overview of our proofs.

The Gowers norm metric can characterize affine-invariant parameters of functions, making them constant-query estimable and testable for properties like constant spectral norm and degree …

Apr 1, 2022 · We establish a link between the Gowers norm and our pseudorandom measure, and show that “good” pseudorandom subsets must have “small” Gowers norm. We give an …

Rosemary Millicent Ward, Viscountess Ednam ARRC (née Sutherland-Leveson-Gower, 9 August 1893 – 21 July 1930) was a British socialite who served as a nurse in France during the First …