Trigonometric series with gaps and the Fourier restriction problem

 Abstract: 

The 1950s was a golden age in harmonic analysis with the development of two perspectives:

 (1) Harmonic analysis on locally compact abelian groups and

 (2) Calderon-Zygmund theory 

In this talk we make a connection between the two. We revisit theories of various thin sets in harmonic analysis developed by W. Rudin in the 1950s and reformulate these theories in the context of Fourier restriction, a fundamental problem in euclidean harmonic analysis introduced by E.M. Stein in the 1960s.