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Vector-valued multipliers: convolution with operator-valued measures

Gaudry G. I.; Ricker W. J.; Jefferies B. R. F.

  • 2000

Abstract

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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.

How to cite

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Gaudry G. I., Ricker W. J., and Jefferies B. R. F.. Vector-valued multipliers: convolution with operator-valued measures. 2000. <http://eudml.org/doc/275830>.

@book{GaudryG2000,
abstract = { 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.},
author = {Gaudry G. I., Ricker W. J., Jefferies B. R. F.},
keywords = {multipliers; Fourier-Stieltjes transforms; spectral measures; Calderon-Zygmund theory; vector-valued singular integral operators; vector-valued convolution operators; Coste's theorem; Brenner's theorem},
language = {eng},
title = {Vector-valued multipliers: convolution with operator-valued measures},
url = {http://eudml.org/doc/275830},
year = {2000},
}

TY - BOOK
AU - Gaudry G. I.
AU - Ricker W. J.
AU - Jefferies B. R. F.
TI - Vector-valued multipliers: convolution with operator-valued measures
PY - 2000
AB - 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.
LA - eng
KW - multipliers; Fourier-Stieltjes transforms; spectral measures; Calderon-Zygmund theory; vector-valued singular integral operators; vector-valued convolution operators; Coste's theorem; Brenner's theorem
UR - http://eudml.org/doc/275830
ER -

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