Almost-Periodic Algebras and Their Automorphisms

The problem concerning the form of the maximal ideal space of an almost-periodic algebra formed by functions on $\mathbb{R}^m$ is considered. It is shown that this space is homeomorphic to the topological group dual to the group of frequencies of the algebra under consideration. In the case of a quasiperiodic algebra, the mappings of $\mathbb{R}^n$ generating automorphisms of the algebra are described. Several specific examples are given and a relation to the theory of quasicrystals is indicated.