Defence of doctoral thesis in the field of mathematics, LicSc (Tech) Diana Andrei
‘Extensions of the multicentric functional calculus’ touches a key concept in operator theory, that is, the spectrum of an operator. Multicentric functional calculus shows that there is a simple way to do complex analysis on complicated sets by using a change of variable.
The change of variables aims to present functions in simple forms. Incorporating a polynomial as a new global variable for an analytic function has not been used because polynomials have several roots and their values when mapped are overlapping, resulting in loss of information. In 2012 Olavi Nevanlinna presented a simple way to avoid the loss of information, allowing complex sets to be mapped in the disk, and after the analysis is done, to go back to the original set. An example of a complex set where an analytic function is efficiently represented is the spectrum of a continuous operator. When the neighborhood is mapped by a polynomial lemniscate inside a small disk, then we have an effective so-called multicentric functional calculus.
My work concerns generalizations of this multicentric functional calculus, such as using rational functions instead of polynomials and see what extra information that brings, or how this calculus becomes more common in the case of multiple commuting operators.
Opponent is Doctor Jari Taskinen, University of Helsinki, Finland
Custos is Professor Juha KinnunenAalto University School of Science, Department of Mathematics and Systems Analysis
Contact details of the doctoral student: [email protected], 0409669791
The public defence will be organised on campus.
The doctoral thesis is publicly displayed 10 days before the defence in the publication archive Aaltodoc of Aalto University.