Date of Award
2019
Publication Type
Master Thesis
Degree Name
M.Sc.
Department
Mathematics and Statistics
Supervisor
Mehdi Monfared
Rights
info:eu-repo/semantics/openAccess
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Abstract
We study the definition and properties of almost periodic functions on topological groups. We show the equivalence between Bochner’s and Bohr’s definitions of almost periodicity. We discuss Weil’s construction of Bohr compactification b(G) and study its properties. Using Peter-Weyl’s density theorem we show that a function f in Cb(G) is almost periodic if and only if it is the uniform limit of linear combinations of coefficients of the finite-dimensional irreducible unitary representations of G. We show the existence of a unique invariant mean on the space of almost periodic functions. We investigate the Fourier series of almost periodic functions, and show that it extends the classical Fourier series of 2-periodic functions.
Recommended Citation
Zhu, Yihan, "Almost Periodic Functions on Topological Groups" (2019). Electronic Theses and Dissertations. 7748.
https://scholar.uwindsor.ca/etd/7748