Kashiwara M.  Systems of microdifferential equations

Название: 
Systems of microdifferential equations 
Автор: 
Kashiwara M. 
Категория: 
Математика

Тип: 
Книга 
Дата: 
04.01.2009 12:19:23 
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Описание: 
This book grew out from a course that Masaki Kashiwara gave at the "Universite ParisNord" during the first term of the academic year 197677. Teresa Honteiro Fernandes worked out lecture notes for this course, which were preprinted in 1979 by ParisMord under the title "Systemes d'equations microdiffentielles" and distributed to a happy few. On the grounds that such a basic textbook should be made available to a wider mathematical audience, the Birkhauser Publishing Company proposed to make it a new volume of its series "Progress in Mathematics". Kashiwara and the publisher agreed not to change the overall structure of the text (which at first was supposed to be provisional); T. Monteiro Fernandes then was kind enough to take care of the translation into English and of the necessary minor corrections.
It was decided that an introduction might be written, outlining the purposes and main features of the text, and mentioning recent developments connected with the index formula in Chapter 6. Kashiwara suggested that I would write this introduction, and I accepted to do so with pleasure. I thought it might be a way of thanking Kashiwara for all he has taught me since I benefited so much from talking to him and reading his works.
In short, this book is an introduction to systems of microdifferential equations and to some of the tools of microlocal analysis. Here a remark on the terminology; after [Boutet de MonveJKree] , pseudodifferential operators on a complex manifold X were considered in f4 : They used the notation (P for the sheaf of rings of pseudodifferential operators (this was a sheaf on the projectivized contangent bundle of X). In recent years, instead of L'j, one has been using ~Zl (now viewed as a sheaf of rings on the cotangent bundle itself); "K, is called the sheaf of microdi fferential operators: microdifferential operators are defined and studied locally in the cotangent bundle, i.e. microlocally.
As is wellknown, say for X of complex dimension one with variable t, both r and (7) are microdifferential operators (more pre 
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