Additive Decomposability of Functions over Abelian Groups

Independence, Decomposability and Functions which Take Values into an Abelian Group

Decomposition is an important property that we exploit in order to render problems more tractable. The decomposability of a problem implies the existence of some “independences” between the variables that are in play in the problem under consideration. In this paper we investigate the decomposability of functions which take values into an Abelian Group. For the problems which involve these type...

Shift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups

We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range funct...

Additive Bases in Groups

We study the problem of removing an element from an additive basis in a general abelian group. We introduce analogues of the classical functions X,S and E (defined in the case of N) and obtain bounds on them. Our estimates on the functions SG and EG are valid for general abelian groups G while in the case of XG we show that distinct types of behaviours may occur depending on G.

On the Finite Groups that all Their Semi-Cayley Graphs are Quasi-Abelian

In this paper, we prove that every semi-Cayley graph over a group G is quasi-abelian if and only if G is abelian.

A Decomposition for Complete Normed Abelian Groups with Applications to Spaces of Additive Set Functions