A project aiming to develop mathematical theories from the 19th century

Bartosz Malman, Assistant Professor of Mathematics at MDU, is leading a project that aims to develop Fourier analysis, a mathematical theory from the 19th century.

In the early 1800s, the French mathematician Joseph Fourier studied the mathematical theory of heat transfer. In connection with this, he had the ingenious, but at the time highly controversial idea that mathematical functions should be able to be constructed as an infinite sum of elementary sine waves with different oscillation frequencies. The theory, which has proven to be reliable, is called Fourier analysis and has a significant impact on mathematics, natural sciences, and engineering to this day.

Bartosz Malman is leading the project Hunting for Traces of Analyticity with Applications in Operator Theory, which has been granted four million kronor to investigate and develop the principles of Fourier analysis. He examines the frequency spectrum for certain classes of mathematical functions and tries to find the limit of how dispersed the frequencies can be.

I am interested in determining the structure of the frequency spectrum for certain classes of mathematical functions. The goal is to develop mathematical tools that can be applied more generally, says Bartosz.

Today, Fourier analysis is used, among other things, to filter out unnecessary noise from signals, and in quantum physics, it is used to formalize Heisenberg's uncertainty relations.

Fourier analysis is an astonishingly successful theory that continues to amaze with its wide-ranging applications. In the project, we want to further develop the mathematics itself and deepen the theory to find new areas of application, says Bartosz.