October 2022 Power series as Fourier series
Debraj Chakrabarti, Anirban Dawn
Rocky Mountain J. Math. 52(5): 1539-1574 (October 2022). DOI: 10.1216/rmj.2022.52.1539

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.

Citation

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Debraj Chakrabarti. Anirban Dawn. "Power series as Fourier series." Rocky Mountain J. Math. 52 (5) 1539 - 1574, October 2022. https://doi.org/10.1216/rmj.2022.52.1539

Information

Received: 8 July 2021; Revised: 24 December 2021; Accepted: 25 December 2021; Published: October 2022
First available in Project Euclid: 28 November 2022

MathSciNet: MR4563735
zbMATH: 1510.32001
Digital Object Identifier: 10.1216/rmj.2022.52.1539

Subjects:
Primary: 22D12 , 32A05

Keywords: abstract Fourier series , Cauchy–Riemann equations , Laurent series , Reinhardt domains , Taylor series

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

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Vol.52 • No. 5 • October 2022
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