Special function spaces for special functions

Adem Limani will receive his doctoral degree in mathematics from Lund University in 2022. Thanks to a grant from the Knut and Alice Wallenberg Foundation, he will hold a postdoctoral position with Professor Artur Nicolau at the Universitat Autònoma de Barcelona, Spain.

Adem Limani’s research focuses on mathematical analysis, which is one of the oldest branches of mathematics and has roots in Antiquity. Despite its long history, mathematical analysis has recently received a great deal of attention, with new problems that require unconventional combinations of tools from different areas of mathematics, such as complex and harmonic analysis, functional analysis and operator theory. This also applies to the planned project.

Many physical phenomena can be described using linear operators. An operator is a function that represents a mathematical operation, which could be as simple as a plus or a minus, or considerably more complex, where functions are transformed using an operator.

Many different types of function spaces, which comprise multitudes of functions, are studied in mathematics. Of particular interest in this project is a space that consists of all the analytical functions on a unit disc that are obtained after having transformed some functions with an operator. Understanding the different properties of the functions included in a function space is often of interest, and there are many open problems in the specific space relevant to this project. The purpose of the project is to develop methods for when and how to construct functions that extend continuously to the boundary of the unit disc and to study the theoretical functional properties of these space.