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 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...

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in this paper, we investigate the relation between l-projections and conditional expectations on subalgebras of the fourier-stieltjes algebra b(g), and we will show that compactness of g plays an important role in this relation.

‎In this note‎, ‎we consider the concentration function problem for a continuous action of a locally compact group $G$ on a locally compact Hausdorff space $X$‎. ‎We prove a necessary and sufficient condition for the concentration functions of a‎ ‎spread-out irreducible probability measure $mu$ on $G$ to converge to zero.

‎We prove that a remainder $Y$ of a non-locally compact‎ ‎rectifiable space $X$ is locally a $p$-space if and only if‎ ‎either $X$ is a Lindel"{o}f $p$-space or $X$ is $sigma$-compact‎, ‎which improves two results by Arhangel'skii‎. ‎We also show that if a non-locally compact‎ ‎rectifiable space $X$ that is locally paracompact has a remainder $Y$ which has locally a $G_{delta}$-diagonal‎, ‎then...