157 citations · 642 across the 35 of their papers we have counts for
5 papers · 2 filters
A quantitative version of the idempotent theorem in harmonic analysis
Ben Green, Tom Sanders
Suppose that G is a locally compact abelian group, and write M(G) for the algebra of bounded, regular, complex-valued measures under convolution. A measure μin M(G) is said to be i…
An application of a local version of Chang's theorem
Tom Sanders
We prove a theorem claimed in math.CA/0605519 which asserts that if A is a subset of a compact abelian group G with density of a particular (natural, although technical) form then…
Boolean functions with small spectral norm
Ben Green, Tom Sanders
Suppose that f is a boolean function from F_2^n to {0,1} with spectral norm (that is the sum of the absolute values of its Fourier coefficients) at most M. We show that f may be ex…
The Littlewood-Gowers problem
Tom Sanders
We show that if A is a subset of Z/pZ (p a prime) of density bounded away from 0 and 1 then the A(Z/pZ)-norm (that is the l^1-norm of the Fourier transform) of the characterstic fu…
The l^1-norm of the Fourier transform on compact vector spaces
Tom Sanders
Suppose that A is a subset of F_2^n of density as close to 1/3 as possible. We show that the A(F_2^n)-norm (that is the sum of the absolute values of the Fourier transform) of the…