%0 Journal Article
%T Some applications of W. Rudin's inequality to problems of combinatorial number theory
%A Ilya D. Shkredov
%J Uniform Distribution Theory
%D 2011
%I Mathematical Institute of the Slovak Academy of Sciences
%X 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.
%K Abelian group
%K matrix
%K singular
%K eigenvalue
%K prime
%K Fourier transformation
%U http://www.boku.ac.at/MATH/udt/vol06/no2/08Shkredov11-2.pdf