Markus Gustafsson: On holomorphic functions; analytic continuation, boundary values on the disk of convergence and the Hardy spaces

Abstract

In this thesis we are looking at holomorphic functions, their connection to power series and behaviour on the boundary of the disk of convergence. We investigate analytic continuation with several examples, displaying how one can use the Poisson kernel to analyse values on, or restore a function from, the boundary of the disk of convergence. We are also going to explore some theory of the Hardy spaces on the unit disk.

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