An Excursion into Fourier Analysis: An Interview with Mahdi Hormozi

Elsewhere, the history and introduction of harmonic analysis into Iran hasbeen briefly discussed. Abstract harmonic analysis is, without doubt, a natural extensionof the Fourier’s series and integrals. It’s worth noting that Harmonic analysis isnothing 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 fromFourier’s treatise into the 1950s, focused mainly on investigating the convergence andsummability methods of Fourier series. The modern era of Fourier analysis was essentiallyshaped by Lebesgue’s theory of integration and the introduction of the concept ofabstract function spaces, thus shifting the focus from examining individual members ofa space of functions to investigating the entire space. This era was further developed inFourier analysis by Antoni Zygmund’s introduction of real variable methods. AlbertoCalderon’s contributions began in the 1950s.In the first part of this paper, we briefly survey the most critical developmentsin 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 ChalmersUniversity of Technology– provides us with a more rigorous picture of the modern eraof Fourier analysis.