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A Short Introduction to Perturbation Theory for Linear Operators (Paperback, Softcover reprint of the original 1st ed. 1982)
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A Short Introduction to Perturbation Theory for Linear Operators (Paperback, Softcover reprint of the original 1st ed. 1982)
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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."
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