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

Abstract

In the paper we obtain some new applications of well--known W. Rudin's theorem concerning lacunary series to problems of combinatorial number theory. We generalize a result of M.-C. Chang on L_2 (L)-norm of Fourier coefficients of a set (here L is a dissociated set), and prove a dual version of the theorem. Our main instrument is computing of eigenvalues of some operators.

15 pages

References in corpus (3)

• On sets with small doubling
• An application of a local version of Chang's theorem
• Some examples of sets of large exponential sums

Cited by in corpus (1)

• Some new inequalities in additive combinatorics