Modern Birkhauser Classics
2 total works
This volume serves as an introduction to the subject of Fourier integral operators. Covering a range of topics from Hormander's exposition of the theory, Duistermaat approaches the subject of symplectic geometry, and includes applications to hyperbolic equations (equations of wave type).
The Heat Kernel Lefschetz Fixed Point Formula for the Spin-C Dirac Operator
by J J Duistermaat
Published December 1995
When visiting M.I.T. for two weeks in October 1994, Victor Guillemin made me enthusiastic about a problem in symplectic geometry which involved the use of the so-called spin-c Dirac operator. Back in Berkeley, where I had l spent a sabbatical semester, I tried to understand the basic facts about this operator: its definition, the main theorems about it, and their proofs. This book is an outgrowth of the notes in which I worked this out. For me this was a great learning experience because of the many beautiful mathematical structures which are involved. I thank the Editorial Board of Birkhauser, especially Haim Brezis, for sug gesting the publication of these notes as a book. I am also very grateful for the suggestions by the referees, which have led to substantial improvements in the presentation. Finally I would like to express special thanks to Ann Kostant for her help and her prodding me, in her charming way, into the right direction. J.J. Duistermaat Utrecht, October 16, 1995."