The purpose of these lectures is to discuss some results, both classical and recent, on non-harmonic Fourier series as well as related results on sampling and interpolating in spaces of entire functions.
Among other topics we are going to discuss:
-- Riesz bases of exponential functions in L^2(-\pi,\pi)
and complete interpolating sequences in the Paley-Wiener spaces;
-- relation between interpolation problems in spaces of entire
functions and the Hilbert transform;
-- stability of Riesz bases of exponential functions;
-- frames of exponentials, Beurling's theorem on interpolation and
balayage;
-- Riesz bases of exponential functions on a system of intervals and
matrix Wiener-Hopf operator;
-- Fourier series on convex symmetric polygons;
-- Gabor frames and interpolation in Bargmann-Fock space.