xii PREFACE Several excellent treatments of semiclassical analysis have appeared re- cently. The book [D-S] by Dimassi and Sj¨ ostrand starts with the WKB- method, develops the general semiclassical calculus, and then provides high- tech spectral asymptotics. Martinez [M] provides a systematic development of FBI transform techniques, with applications to microlocal exponential estimates and to propagation estimates. This text is intended as a more elementary, but much broader, introduction. Except for the general symbol calculus, for which we followed Chapter 7 of [D-S], there is little overlap with these other two texts or with the influential books by Helffer [He] and by Robert [R]. Guillemin and Sternberg [G-St1] offer yet another perspec- tive on the subject, very much complementary to that given here. Their notes concentrate on global and functorial aspects of semiclassical analy- sis, in particular on the theory of Fourier integral operators and on trace formulas. The approach to semiclassical analysis presented here is influenced by my long collaboration with Johannes Sj¨ ostrand. I would like to thank him for sharing his philosophy and insights over the years. I first learned microlocal analysis from Richard Melrose, Victor Guillemin, and Gunther Uhlmann, and it is a pleasure to acknowledge my debt to them. Discussions of semi- classical physics and chemistry with St´ ephane Nonnenmacher, Paul Brumer, William H. Miller, and Robert Littlejohn have been enjoyable and valuable. They have added a lot to my appreciation of the subject. I am especially grateful to St´ ephane Nonnenmacher, Semyon Dyatlov, Claude Zuily, Oran Gannot, Xi Chen, Hans Christianson, Jeff Galkowski, Justin Holmer, Long Jin, Gordon Linoff, and Steve Zelditch for their very careful reading of the earlier versions of this book and for their many valuable comments and corrections. My thanks also go to Faye Yeager for typing the original lecture notes and to Jonathan Dorfman for TEX advice. Stephen Moye at the AMS pro- vided fantastic help on deeper TEX issues and Arlene O’Sean’s excellent copyediting removed many errors and inconsistencies. I will maintain on my website at the UC Berkeley Mathematics De- partment http://math.berkeley.edu/~zworski a list of errata and cor- rections, as well as at the American Mathematical Society’s website www.ams.org/bookpages/gsm-138. Please let me know about any errors you find. I have been supported by NSF grants during the writing of this book, most recently by NSF grant DMS-0654436. Maciej Zworski
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