Mathematical Culture and Thought

Mathematical Culture and Thought

An Excursion into Fourier Analysis: An Interview with Mahdi Hormozi

Document Type : Review

Author
S. Maghsoudi
Department of Mathematics, University of Zanjan, Iran
10.30504/mct.2023.1378.1968
Abstract
Elsewhere, the history and introduction of harmonic analysis into Iran has
been briefly discussed. Abstract harmonic analysis is, without doubt, a natural extension
of the Fourier’s series and integrals. It’s worth noting that Harmonic analysis is
nothing but the development of the theory of series and integrals on topological groups
(or similar structures). The history of Fourier analysis can be divided into two periods:
classical and modern. The classical period of Fourier analysis, which spanned from
Fourier’s treatise into the 1950s, focused mainly on investigating the convergence and
summability methods of Fourier series. The modern era of Fourier analysis was essentially
shaped by Lebesgue’s theory of integration and the introduction of the concept of
abstract function spaces, thus shifting the focus from examining individual members of
a space of functions to investigating the entire space. This era was further developed in
Fourier analysis by Antoni Zygmund’s introduction of real variable methods. Alberto
Calderon’s contributions began in the 1950s.
In the first part of this paper, we briefly survey the most critical developments
in Fourier analysis from the early days till recent decades. Then, in the second part,
an interview with M. Hormozi –a Fourier analyst who graduated from the Chalmers
University of Technology– provides us with a more rigorous picture of the modern era
of Fourier analysis.
Keywords
Fourier analysis
Fourier series
singular integrals
Hilbert transform
BMO spaces
PhD programmes in Sweden

Subjects

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  • Receive Date 05 March 2023
  • Accept Date 25 May 2023
  • Publish Date 22 June 2023