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Search: All articles in the CMB digital archive with keyword Fourier analysis

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1. CMB 2011 (vol 56 pp. 412)

Sanders, T.
 Structure in Sets with Logarithmic Doubling Suppose that $G$ is an abelian group, $A \subset G$ is finite with $|A+A| \leq K|A|$ and $\eta \in (0,1]$ is a parameter. Our main result is that there is a set $\mathcal{L}$ such that \begin{equation*} |A \cap \operatorname{Span}(\mathcal{L})| \geq K^{-O_\eta(1)}|A| \quad\text{and}\quad |\mathcal{L}| = O(K^\eta\log |A|). \end{equation*} We include an application of this result to a generalisation of the Roth--Meshulam theorem due to Liu and Spencer. Keywords:Fourier analysis, Freiman's theorem, capset problemCategory:11B25

2. CMB 2011 (vol 56 pp. 218)

Yang, Dilian
 Functional Equations and Fourier Analysis By exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations - the d'Alembert equation, the Wilson equation, and the d'Alembert long equation - on compact groups. Keywords:functional equations, Fourier analysis, representation of compact groupsCategories:39B52, 22C05, 43A30