Surveys in analysis & operator theory
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About
Preface
This volume contains survey articles based on lecture series given by the authors at The Australian National University between July 2001 and June 2002. All but one were given in the seminar series of the Special Program on Spectral and Scattering Theory which was held at ANU from July to December, 2001. The exception is the article by Ben Andrews, which is based on lectures given in the regular geometry/analysis seminar at ANU during the first half of 2002. All the articles have an expository character, generally including either new results or very recently published material.
The Special Program on Spectral and Scattering Theory was an activity of the CMA, organised by Alan McIntosh and myself. The main activities of the Special Program were two National Research Symposia held during August and September, and a seminar series held on Tuesday and Thursday afternoons for the duration of the Program. A number of distinguished visitors in this field (about 16 in all) were invited to ANU for up to six weeks, to give either a series of lectures or symposium talks. The scope of the Program was interpreted broadly to include harmonic analysis, partial differential equations and operator theory as well as spectral and scattering theory.
On behalf of the CMA, I wish to thank the authors of these surveys for their contribution to the Special Program and to this volume of the Proceedings of the CMA. I also thank the CMA’s administrative staff, Annette Hughes and Kate McKay, for their help in the smooth running of the Special Program, and Terry Tao for co-organising the National Research Symposia.
Each article in this volume was refereed.
Professor Andrew Hassell
Content
| Chapter | Page | |
|---|---|---|
| 1 | Lectures on the Kato Square Root Problem Pascal Auscher | 1 |
| 2 | Low-regularity global solutions to nonlinear dispersive equations Terence Tao | 19 |
| 3 | L2 harmonic forms on non-compact Riemannian manifolds Gilles Carron | 49 |
| 4 | Lectures on scattering theory Dmitri Yafaev | 61 |
| 5 | Dilation of contractive tuples: a survey Tirthankar Bhattacharyya | 89 |
| 6 | Resonance quantum switch: matching domains Boris Pavlov | 127 |
| 7 | Notes on the Isometric Embedding Problem and the Nash-Moser Implicit Function Theorem Ben Andrews | 157 |
Copyright statement
First published in Australia 2002
© Centre for Mathematics and its Applications
Mathematical Sciences Institute
The Australian National University
CANBERRA ACT 0200
AUSTRALIA
This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.
Edited by
Andrew Hassell
Centre for Mathematics and Its Applications, The Australian National University
Surveys in Analysis and Operator Theory
ISBN 0 7315 5204 0