A course on topological groups (Q5906348)

The aim of the book is a self-contained proof of the Peter-Weyl theorem. The author follows the classical approach and gradually builds all necessary topological, analytical and algebraic ingredients. After a very brief introduction to topological spaces and topological groups in Chapter 1, Haar measure and \(L^1\)-algebras of locally compact groups are discussed in Chapter 2, while Chapter 3 is dedicated to Hilbert spaces and the spectral theorem. The last Chapter 4 contains the proof of Peter-Weyl's theorem and its connection to the Bohr's theorem on almost periodic functions. No further applications are given, in particular no connection to the Pontryagin duality theorem is mentioned at all.