Tosio Kato – författare

This book is a slightly expanded reproduction of the first two chapters (plus Introduction) of my book Perturbation Theory tor Linear Operators, Grundlehren der mathematischen Wissenschaften 132, Springer 1980. Ever since, or even before, the publication of the latter, there have been suggestions about separating the first two chapters into a single volume. I have now agreed to follow the suggestions, hoping that it will make the book available to a wider audience. Those two chapters were intended from the outset to be a comprehen­ sive presentation of those parts of perturbation theory that can be treated without the topological complications of infinite-dimensional spaces. In fact, many essential and. even advanced results in the theory have non­ trivial contents in finite-dimensional spaces, although one should not forget that some parts of the theory, such as those pertaining to scatter­ ing. are peculiar to infinite dimensions. I hope that this book may also be used as an introduction to linear algebra. I believe that the analytic approach based on a systematic use of complex functions, by way of the resolvent theory, must have a strong appeal to students of analysis or applied mathematics, who are usually familiar with such analytic tools.

In view of recent development in perturbation theory, supplementary notes and a supplementary bibliography are added at the end of the new edition. Due to these changes, some theorems, lemmas, and formulas of the first edition are missing from the new edition while new ones are added.