@article{ce6985060ff4411bbaf512a8ac115a94,
title = "POWER SERIES AS FOURIER SERIES",
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 = "Cauchy-Riemann equations, Laurent series, Reinhardt domains, Taylor series, abstract Fourier series",
author = "Debraj Chakrabarti and Anirban Dawn",
note = "Funding Information: Debraj Chakrabarti was partially supported by Simons Foundation Collaboration Grant number 706445. 2020 AMS Mathematics subject classification: 22D12, 32A05. Keywords and phrases: Reinhardt domains, abstract Fourier series, Taylor series, Laurent series, Cauchy–Riemann equations. Received by the editors on July 8, 2021, and in revised form on December 24, 2021. Publisher Copyright: {\textcopyright} Rocky Mountain Mathematics Consortium.",
year = "2022",
month = oct,
doi = "10.1216/rmj.2022.52.1539",
language = "English",
volume = "52",
pages = "1539--1574",
journal = "Rocky Mountain Journal of Mathematics",
issn = "0035-7596",
publisher = "Rocky Mountain Journal of Mathematics",
number = "5",
}