Power series as Fourier series

Abstract

An abstract theory of Fourier series in locally convex topological vector spaces is developed. An analog of Fejér's theorem is proved for these series. The theory is applied to distributional solutions of Cauchy-Riemann equations to recover basic results of complex analysis. Some classical results of function theory are also shown to be consequences of the series expansion.

Some spelling mistakes and minor typos corrected. To appear in the Rocky Mountain Journal