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LCALife Cycle Assessment
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References in periodicals archive ?
The abbreviation BSE stands for Bochner-Schoenberg-Eberlin and refers to a famous theorem, proved by Bochner and Schoenberg [3,14] for the additive group of real numbers and in general by Eberlein [6] for a locally compact abelian group G, saying that, in the above terminology, the group algebra [L.sup.1](G) is a BSE algebra.
His topics are Banach analysis and spectral theory, locally compact groups, basic representation theory, analysis of locally compact abelian groups, analysis on compact groups, induced representations, and further topics in representation theory.
For a locally compact abelian group G, Gilbert [15] characterized [weak.sup.*]-closed translation invariant complemented subspaces of [L.sup.[infinity]](G) by their spectra.
Let G be a locally compact abelian group, and let A be a left Banach G-module.
He proceeds from the elementary theory of Fourier series and Fourier integrals to abstract harmonic analysis on locally compact abelian groups.
The symmetries that underlie Shannon's sampling theorem and its more general multi-band version are used as a basis for an exposition of sampling theory in a locally compact abelian group setting.
Key words and phrases: Whittaker-Kotel'nikov-Shannon theorem, Plancherel's formula, locally compact abelian groups, discrete subgroups, tranvsersals
These very different groups R, [T.sup.1], Z are all abelian and locally compact ([T.sup.1] is compact), and so are united by working with locally compact abelian groups.
However we shall be concerned with locally compact abelian groups, where the theory has close analogues with the classical theory and is particularly well suited to sampling theory.
the direct limit of locally compact abelian groups, is equipped with a continuous action of [GAMMA] = [[GAMMA].sub.F].
Any locally compact abelian group M defines a sheaf yM of abelian groups on Top; this (Yoneda) provides a fully faithful embedding of the (additive, but not abelian) category Tab of locally compact abelian groups into the (abelian) category Tab of sheaves of abelian groups on Top.
The abbreviation BSE stands for Bochner-Schoenberg-Eberlein and refers to the famous theorem, proved by Bochner and Schoenberg [2,18] for the additive group of real numbers and in general by Eberlein [6] for locally compact abelian groups G, saying that, in the above terminology, the group algebra [L.sup.1] (G) is a BSE-algebra (See [17] for a proof).
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