Power series as Fourier series
Complex Variables
2022-10-25 v2
Abstract
An abstract theory of Fourier series in locally convex topological vector spaces is developed. An analog of Fej\'{e}r'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.
Keywords
Cite
@article{arxiv.2107.04201,
title = {Power series as Fourier series},
author = {Debraj Chakrabarti and Anirban Dawn},
journal= {arXiv preprint arXiv:2107.04201},
year = {2022}
}
Comments
Some spelling mistakes and minor typos corrected. To appear in the Rocky Mountain Journal