Results 191 to 200 of about 1,273 (222)
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On the Frames of Translates on Locally Compact Abelian Groups
Bulletin of the Iranian Mathematical Society, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Najmeh Sadat Seyedi +1 more
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ON THE ABELIAN EXTENSIONS OF LOCALLY COMPACT ABELIAN GROUPS
Mathematics of the USSR-Sbornik, 1982The group of all abelian extensions of a compact abelian group by a discrete abelian group is calculated completely. Criteria are found for the vanishing of the group of all abelian extensions of a discrete abelian group by a compact one. Two criteria for the splitting of compact abelian groups are obtained.
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Nonstandard analysis and locally compact Abelian groups
Acta Applicandae Mathematicae, 1991The author presents a method of nonstandard analysis for constructing separable locally compact abelian (LCA) groups. He also defines the notion of hyperfinite approximation of LCA-groups and shows that every separable LCA group has an admissible hyperfinite approximation.
E I Gordon
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On the Approximation of Functions on Locally Compact Abelian Groups
Georgian Mathematical Journal, 1999Abstract Questions of approximative nature are considered for a space of functions πΏπ(πΊ, ΞΌ), 1 β€ π β€ β, defined on a locally compact abelian Hausdorff group πΊ with Haar measure ΞΌ. The approximating subspaces which are analogs of the space of exponential type entire functions are introduced.
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Locally Compact Abelian Groups
1985Section 1 constructs Haar measure on a locally compact group G, by a method of H. Cartan. Certain least upper bounds must be proved to exist in order to make the classical proof constructive; this adds length to the classical treatment. In Section 2 convolution is defined and the group algebra is studied.
Errett Bishop, Douglas Bridges
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Semigroup completions of locally compact Abelian groups
Topology and its Applications, 2019A topological group is {\em absolutely closed} if it is closed in every topological group containing it as a subgroup and a topological semigroup \(S\) is said to be {\em absolutely closed} in a class \(\mathcal{G}\) of topological semigroups, if \(S\) is closed in every semigroup \(T\in \mathcal{G}\) containing \(S\) as a subsemigroup.
Keyantuo, Valentin, Zelenyuk, Yevhen
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Orthogonal wavelets on locally compact Abelian groups
Functional Analysis and Its Applications, 1997Consider a pair \((G,A)\), where \(G\) is a locally compact Abelian group, \(H\) is a discrete subgroup of \(G\) such that the quotient group \(G/H\) is compact and \(A\) is an automorphism of \(G\) such that \(A(H)\) is a proper subgroup of \(H\). Denote \(L^2(G,\mu)\), where \(\mu\) is the Haar measure on \(G\), by \(L^2(G)\).
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Universal symbols on locally compact Abelian groups
Functional Analysis and Its Applications, 2013A symbol on a dual group \(X\) is a function \(f\) such that \(f|Q=\hat{\mu}|Q\), for each compact set \(Q\subset X\), where \(\hat{\mu}\) is the Fourier transform of some measure \(\mu\). For each compact set \(Q\subset X\), let \(B(Q)\) be the Bernstein space of functions whose Fourier transforms are supported on \(Q\).
Gorin, E. A., Norvidas, S.
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PEGO THEOREM ON LOCALLY COMPACT ABELIAN GROUPS
Journal of Algebra and Its Applications, 2014In this paper, we show the version of Pego's theorem on locally compact abelian groups. This theorem, [R. L. Pego, Compactness in L2 and the Fourier transform, Proc. Amer. Math. Soc.95 (1985) 252β254], gives a characterization of precompact sets of L2 in terms of the Fourier transform.
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On a characterization theorem for locally compact abelian groups
Probability Theory and Related Fields, 2005Let \(X\) be a locally compact Abelian separable metric group containing no elements of order two. Let \(\xi_j\), \(j=1,2,\ldots ,n\), \(n\geq 2\), be independent \(X\)-valued random variables having distributions \(\mu_j\) with non-vanishing characteristic functions. Suppose that \[ \alpha_j,\beta_j\in \text{Aut}(X)\text{ and }\beta_i\alpha_i^{-1}\pm \
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