Real Analysis Exchange

A Didactic Note on Classic Function Spaces and the Fourier Transform

Sandra Lucente

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In the present paper we recall the main points of the Fourier Transform developments, in particular the historical origin of the inversion formula. Hence we construct explicit examples of functions in different zones of the range of the Fourier transform in \(L^1\). These can be used as exercises in a basic course of signal processing or harmonic analysis.

Article information

Real Anal. Exchange, Volume 44, Number 1 (2019), 229-246.

First available in Project Euclid: 27 June 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 97C70: Teaching-learning processes

Didactic for University Fourier Transform Function spaces


Lucente, Sandra. A Didactic Note on Classic Function Spaces and the Fourier Transform. Real Anal. Exchange 44 (2019), no. 1, 229--246. doi:10.14321/realanalexch.44.1.0229.

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