Doctoral Defense in Mathematics - Bergur Snorrason

Doctoral candidate:
Bergur Snorrason

Title of thesis:
Restricted and weighted polynomial approximations

Opponents:
Dr. Alexander Rashkovskii, Professor at the Department of Mathematics and Physics, Universitetet i Stavanger, Norway, Dr. Lars Martin Sektnan, Senior Lecturer at the Department of Mathematical Sciences, Göteborgs Universitet

Advisors:
Dr. Benedikt Steinar Magnússon, Associate Professor at the Faculty of Physical Sciences, University of Iceland, Dr. Ragnar Sigurðsson, Professor at the Faculty of Physical Sciences, University of Iceland

Also in the doctoral committee:
Dr. Séverine Biard, Associate Professor at the Faculty of Mathematics, Université Polytechnique des Hauts-de-France, France, Dr. Tyson Ritter, Associate Professor at the Department of Mathematics and Physics, Universitetet i Stavanger, Norway

Chair of Ceremony:
Dr. Birgir Hrafnkelsson, Professor and Head of the Faculty of Physical Sciences, University of Iceland

Abstract:

The thesis contains material from papers studying polynomial approximations of holomorphic functions in several variables. These approximations are weighted, in the sense that the norm used to assess the approximation is weighted, and polynomials used for the approximation are restricted to a certain subring of polynomials. The notion of the degree of a polynomial is also different from the classical setting. The main aim is to develop an analog of the Bernstein-Walsh-Siciak theorem, a quantitative counterpart of the Oka-Weil-Runge theorem. To aid this study the Siciak-Zakharyuta functions, sometimes called global extremal functions or pluricomplex Green functions, from pluripotential theory are generalized. They are then used to construct weights for Hörmander’s L2-estimates of solutions to d-bar-equations and the solutions to those equations are then used to construct the desired polynomials.

About the candidate:
Bergur Snorrason was born in Reykjavík in 1995. He finished his diploma from Borgarholtskóli in 2014. He got a bachelor's degree in Mathematics from the University of Iceland in 2018 and a master's degree in 2020. Bergur lives in Mosfellsbær with his fiancee Sandra Sif, two sons, and a dog.