CONTENTS Preface.........................................................................................................5 1. Introduction...............................................................................................6 1.1. Measurability and vector measures.....................................................6 1.2. Convolution and vector measures.....................................................12 1.3. Operator-valued measures................................................................14 2. Harmonic analysis....................................................................................17 2.1. Commutative harmonic analysis for vector-valued functions...............17 3. Convolution with respect to operator-valued measures...........................24 3.1. General theory....................................................................................24 3.2. Vector-valued p-multipliers..................................................................28 3.3. Characterising operator-valued Fourier-Stieltjes transforms..............44 3.4. Strong 1-multipliers.............................................................................47 3.5. Locally compact groups in general: Wendel's theorem.......................54 3.6. Costé's theorem..................................................................................57 4. Convolution with respect to spectral measures........................................60 4.1. General theory....................................................................................60 4.2. Translation: the canonical spectral measure on L²(G)........................65 4.3. Applications........................................................................................72 References..................................................................................................74 Index............................................................................................................76
2000 Mathematics Subject Classification: Primary 46G10, 42B15; Secondary 43A15, 43A05.
@book{bwmeta1.element.zamlynska-7a144ce8-64ae-46ea-940b-11c8758319b2,
author = {Gaudry G. I. and Ricker W. J. and Jefferies B. R. F.},
title = {Vector-valued multipliers: convolution with operator-valued measures},
series = {GDML\_Books},
year = {2000},
zbl = {0966.46023},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-7a144ce8-64ae-46ea-940b-11c8758319b2}
}
Gaudry G. I.; Ricker W. J.; Jefferies B. R. F. Vector-valued multipliers: convolution with operator-valued measures. GDML_Books (2000), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-7a144ce8-64ae-46ea-940b-11c8758319b2/