The objective of this paper is to construct wavelet packets associated with multiresolution analysis on locally compact Abelian groups. Moreover, from the collection of dilations and translations of the wavelet packets, we characterize the subcollections which form an orthonormal basis for L(G).

Hofmann and Morris [6] proved that a locally compact connected group G has a finite subset generating a dense subgroup if and only if the weight w(G) of G does not exceed c , the cardinality of the continuum. The minimum cardinality of such a topological generating set is an invariant of the group, is denoted by σ(G), and is called the topological rank of G . For compact abelian groups of weigh...

In this paper, we study the group Pext(C, A) for locally compact abelian (LCA) groups A and C. Sufficient conditions are established for Pext(C, A) to coincide with the first Ulm subgroup of Ext(C, A). Some structural information on pure injectives in the category of LCA groups is obtained. Letting C denote the class of LCA groups which can be written as the topological direct sum of a compactl...

A density on a locally compact Abelian group G is a bounded system of compatible measures on the compact quotients of G. The notion of density arises naturally both in connection with the theory of uniform distribution and with the theory of almost periodic functions. Our main result effectively answers the question "when are all densities on G induced by measures on some compactification of G?...

let $pounds$ be the category of all locally compact abelian (lca) groups‎. ‎in this paper‎, ‎the groups $g$ in $pounds$ are determined such that every extension $0to xto yto gto 0$ with divisible‎, ‎$sigma-$compact $x$ in $pounds$ splits‎. ‎we also determine the discrete or compactly generated lca groups $h$ such that every pure extension $0to hto yto xto 0$ splits for each divisible group $x$ ...

We obtain some global features of totally disconnected locally compact (t.d.l.c.) groups G that are isomorphic to a just infinite profinite group, building on an earlier result Barnea–Ershov–Weigel and also using tools developed by P.-E. Caprace, G. Willis the author for studying local structure in t.d.l.c. groups. The approach uses following property groups, essentially due Wilson: given norma...

A locally compact topological group G is called an (H) group if G has a maximal compact normal subgroup with Lie factor. In this note, we study the problem when a locally compact group is an (H) group. Let G be a locally compact Hausdorff topological group. Let G0 be the identity component of G. If G/G0 is compact, then we say that G is almost connected. The structure of almost connected locall...