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Some applications of W. Rudin's inequality to problems of combinatorial number theory

Author(s): Ilya D. Shkredov

Journal: Uniform Distribution Theory
ISSN 1336-913X

Volume: 6;
Issue: 2;
Start page: 95;
Date: 2011;
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Keywords: Abelian group | matrix | singular | eigenvalue | prime | Fourier transformation

In the paper we obtain some new applicationsof well-known W. Rudin's theorem concerning lacunaryseries to problems of combinatorial number theory.We generalize a result of M.-C. Chang on $L_2{\Lambda}$-norm of Fourier coefficients of a set(here $\Lambda$ is a dissociated set),and prove a dual version of the theorem. Our main instrumentis computing of eigenvalues of some operators.
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