Dissertation

Principal algebraic actions of the discrete Heisenberg group

Promotor: Prof.dr. W.T.F. den Hollander, Prof. dr. E.A. Verbitskiy

Author: M. Göll
Date: 30 June 2015
Links: Thesis in Leiden Repository

This thesis studies principal algebraic actions of the discrete Heisenberg group. There are two main questions which are investigated. The first question deals with the problem of finding criteria for a principal algebraic action to be expansive. Expansiveness is directly related to questions about invertibility in the convolution algebra of the discrete Heisenberg group. The results presented in this thesis give a variety of tools which allow one to decide whether an element in the convolution algebra is invertible or not. These findings are based on local principles and the representation theory of the convolution algebra. The second main question which has been addressed is concerned with the search of summable homoclinic points of non expansive actions. This problem was first linked to a deconvolution problem. A method has been introduced to solve such deconvolution problems with the help of abstract harmonic analysis. This method was successfully applied to a certain class of examples.