Titlebook: An Introduction to the Theory of Multipliers; Ronald Larsen Book 1971 Springer-Verlag Berlin · Heidelberg 1971 Koordinatentransformation.M

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https://doi.org/10.1007/978-3-642-92156-8 spaces. In this chapter we shall study a variety of topological linear spaces of functions and measures for which a characterization of the multipliers is relatively accessible. In addition to its intrinsic interest we hope that this material will illustrate some of the differences between the stud

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https://doi.org/10.1007/978-3-642-91143-9vious chapters. In particular, we have already discussed to some extent the cases when .1 and . ∞. Consequently we shall now restrict our attention primarily to the values of . such that 1< . < ∞. We shall show in the following sections that the multipliers for .(.) can, in a certain sense, be repre

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Fragestellungen und Untersuchungsmethoden, algebras. These algebras are similar to the group algebra ..(.) in a great many ways. In particular for noncompact groups we shall see that the algebras ..(.) and ..(.) have the same multipliers. However the algebras ..(.) are neither group nor . algebras. This leads to the observation that the nat

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Prologue: The Multipliers for ,(,), describe those sequences {.} for which.is always the Fourier series of a periodic integrable function whenever.is such a Fourier series. Subsequently the notion has been employed in many other areas of harmonic analysis, such as the study of properties of the Fourier transformation and its extensio

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The Multipliers for Commutative ,*-Algebras,s with the Banach algebra norm, b).c) .* . ≠ 0 if . ≠ 0 and d) <.,.> = <., .* .> for all ., ., .∈.. The standard example of an .*-algebra is the algebra .(.) for a compact group . with the usual convolution multiplication and scalar product. A general discussion of .*-algebras can be found in Loomis

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,The Multipliers for the Pair (, (,), ,(,)), 1 ≦ ,, , ≦ ∞,re . ≠ .. The problem of describing the multipliers in this situation is equally if not more difficult than in the case . = .. In order to obtain a description of the multipliers as convolution operators we shall have to introduce a class of mathematical objects which properly contains the space of