Some theorems on lacunary Fourier series, with extensions to compact groups
Some theorems on lacunary Fourier series, with extensions to compact groups
1. Introduction. 1.1. The theory of lacunary Fourier series, developed by Banach, Kolmogorov, Sidon, Zygmund, and others, deals largely with extraordinary properties that such series possess. The Fourier series for a bounded function converges absolutely if the function has a lacunary Fourier series; an integrable function is square integrable if …