# Transference Methods in Analysis

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*R. R. Coifman; G. Weiss*

A co-publication of the AMS and CBMS

These ten lectures were presented by Guido Weiss at the University of
Nebraska during the week of May 31 to June 4, 1976. They were a part of the
Regional Conference Program sponsored by the Conference Board of the
Mathematical Sciences and funded by the National Science Foundation.

The topic chosen, “the transference method”, involves a very
simple idea that can be applied to several different branches of analysis. The
authors have chosen familiar special cases in order to illustrate the use of
transference: much that involves general locally compact abelian groups can be
understood by examining the real line; the group of rotations can be used to
explain what can be done with compact groups; \(SL(2,\mathbf C)\) plays
the same role vis-à-vis noncompact semisimple Lie groups.

The main theme of these lectures is the interplay between properties of
convolution operators on classical groups (such as the reals, integers, the
torus) and operators associated with more general measure spaces. The basic
idea behind this interplay is the notion of transferred operator; these are
operators “obtained” from convolutions by replacing the translation
by some action of the group (or, in some cases, a semigroup) and give rise,
among other things, to an interaction between ergodic theory and harmonic
analysis. There are illustrations of these ideas.

A graduate student in analysis would be able to read most of this book. The
work is partly expository, but is mostly “self-contained”.

#### Reviews & Endorsements

Details the ‘transference method’ with clarity and plenty of examples.

-- Alberto Torchinsky, Mathematical Reviews

#### Table of Contents

# Table of Contents

## Transference Methods in Analysis

- Cover Cover11 free
- Title i2 free
- Copyright ii3 free
- Contents iii4 free
- Introduction 16 free
- Preface 38 free
- 1. Some Classical Examples of Transference 510 free
- 2. The General Transference Result 1015
- 3. Multipliers Defined by the Action of Locally Compact Abelian Groups 1419
- 4. Transference from the Integers and the Maximal Ergodic Theorem 2025
- 5. Ergodic Flows and the Theory of H[sup(p)] Spaces 2732
- 6. Integral Transforms with Zonal Kernels 3237
- 7. Integral Transforms with Zonal Kernels (Continued) 3742
- 8. Kernels Having Certain Invariance Properties with Respect to Representations of G. 4247
- 9. The Group SL(2, C) 4752
- 10. Some Aspects of Harmonic Analysis on SL(2, C) 5257
- Bibliography 5964
- Back Cover Back Cover167