And Asymptotic Methods Preface
نویسنده
چکیده
I apologize to the mathematical community that it took so long until this book is made available to a greater audience. Originally I planned to extend the material and present, jointly with Jochen Brüning, a larger treatise on geometric analysis. Although this idea is not given up completely, it is a long term project and so I decided to publish this Habilitationsschrift more or less as it is. I made some minor changes due to the suggestions of the referees, I tried to smooth a bit the terrible first English version (in summer 1993 I had to translate the original German manuscript within a few weeks), and I added a summary and some bibliographic notes to each chapter. Still, the reader can hardly overlook that English is not my mother tongue and I apologize in advance for the certainly remaining lingual errors. The reader should be familiar with basic functional analysis and the analysis of ellip-tic operators on compact manifolds. I also assume some familiarity with the asymptotic analysis of the heat trace. The book consists of five chapters. Although the chapters are not completely independent and I suggest to read the book linearly, the book can be divided into two groups of chapters: – Chapters I, II and V present the theory of general Fuchs type differential operators , including the asymptotic analysis of the heat kernel and an index theorem. – Chapters III and IV deal with operators of first and second order. They can be read more or less independently of the other Chapters. Usually I omit the chapter number in the numbering of equations. References like (4.1) are used to refer to equation 4.1 within the same chapter. From another chapter I would use the reference (2.4.1) to refer to equation 4.1 in Chapter II. A few very common notations will be used in the text without explanation. These are listed at the beginning of the list of symbols on page 157. All other notations are explained at their first occurence and they are listed on page 157 with the page number of their first occurence. I curse the day on which I decided to set up names in small caps. Certainly the annoyance reached its climax when I had to change the word " Fuchs " into " Fuchs ". Nevertheless, a book about Fuchs type operators should at least say a few words about …
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تاریخ انتشار 1997