Table Of ContentAdvanced Textbooks in Mathematics ·
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Advanced Textbooks in Mathematics
ISSN: 2059-769X
Published
The Wigner Transform
by Maurice de Gosson
Forthcoming
Periods and Special Functions in Transcendence
by Paula B Tretkoff
Conformal Maps and Geometry
by Dmitry Belyaev
Advanced Textbooks in Mathematics
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Transform
Maurice de Gosson
University of Vienna, Austria
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World Scientific
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Library of Congress Cataloging-in-Publication Data
Names: Gosson, Maurice de.
Title: The Wigner transform I by Maurice de Gosson (University of Vienna, Austria).
Description: New Jersey : World Scientific, 2017. I Series: Advanced textbooks in mathematics
Identifiers: LCCN 20160566801 ISBN 9781786343086 (he : alk. paper) I
ISBN 9781786343093 (pbk : alk. paper)
Subjects: LCSH: Phase space (Statistical physics) I Statistical mechanics.
Classification: LCC QC174.85.P48 G67 20171 DDC 530.15/95--dc23
LC record available at https://lccn.loc.gov/2016056680
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
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Printed in Singapore
To My Charlyne, With All My Love
Preface
The study of the Wigner transform and of its twin brother, the ambiguity
function, has an already long and illustrious history, with strong links
to both pure and applied mathematics, and to physics and engineering.
In this book, we aim at giving a comprehensive and mathematically
rigorous treatment of these subjects at a level which should be accessible
to undergraduate upper~level students in mathematics and mathematical
physics (we have put a special emphasize on the applications to quantum
mechanics, some of them of a rather advanced level). The material should
also be of interest to mathematicians and engineers working in signal
analysis and time-frequency analysis; the confirmed researcher can use this
book as a reference work, since we have tried to unify different topics which
are more or less spread out in the literature.
Needless to saY,' this book is not the first approaching the Wigner
transform using methods from harmonic analysis. Well-cited predecessors
are the comprehensive books by Folland Harmonic Analysis in Phase Space
and by Grochenig Time-Frequency Analysis. The number of contributions
in the form of research or expository papers defies the imagination: we
have not been able to take into account all the recent advances, but rather
focused on the potentially most important; of course these choices do reflect
the author's own tastes.
The book is structured as a series of Lecture Notes; the order in which .
the topics are introduced is therefore linear. I have tried to present the
material using the principle of parsimony, and the mathematics is presented
vii
viii Preface
and structured following the old-fashioned but efficient way Definition -
Lemma - Proposition - Corollary (including, of course, Examples and
Remarks). The chapters are short, and designed for a 60 minutes lecture
(this may be wishful thinking - it depends of course on the initial level
of the audience; I have here in mind upper-level European or American
undergraduates or graduate students).
This work has been financed by the grant P27773-N23 of FWF Der
Wissenschaftsfonds (the Austrian Research Agency)
Maurice A. de Gosson
Vienna, Summer 2016
