## Real Analysis Exchange

### A Didactic Note on Classic Function Spaces and the Fourier Transform

Sandra Lucente

#### Abstract

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

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

Dates
First available in Project Euclid: 27 June 2019

https://projecteuclid.org/euclid.rae/1561622442

Digital Object Identifier
doi:10.14321/realanalexch.44.1.0229

Mathematical Reviews number (MathSciNet)
MR3951344

Zentralblatt MATH identifier
07088973

#### Citation

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. https://projecteuclid.org/euclid.rae/1561622442