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

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.