Author | Kato, Tosio. author |
---|---|

Title | A Short Introduction to Perturbation Theory for Linear Operators [electronic resource] / by Tosio Kato |

Imprint | New York, NY : Springer US, 1982 |

Connect to | http://dx.doi.org/10.1007/978-1-4612-5700-4 |

Descript | XIV, 162 p. online resource |

SUMMARY

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 comprehenยญ 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 nonยญ trivial contents in finite-dimensional spaces, although one should not forget that some parts of the theory, such as those pertaining to scatterยญ 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

CONTENT

One Operator theory in finite-dimensional vector spaces -- ยง 1. Vector spaces and normed vector spaces -- ยง 2. Linear forms and the adjoint space -- ยง 3. Linear operators -- ยง 4. Analysis with operators -- ยง 5. The eigenvalue problem -- ยง 6. Operators in unitary spaces -- ยง 7. Positive matrices -- Two Perturbation theory in a finite-dimensional space -- ยง 1. Analytic perturbation of eigenvalues -- ยง 2. Perturbation series -- ยง 3. Convergence radii and error estimates -- ยง 4. Similarity transformations of the eigenspaces and eigenvectors -- ยง 5. Non-analytic perturbations -- ยง 6. Perturbation of symmetric operators -- ยง 7. Perturbation of (essentially) nonnegative matrices -- Notation index -- Author index

Mathematics
Mathematical analysis
Analysis (Mathematics)
Physics
Mathematics
Analysis
Theoretical Mathematical and Computational Physics