Algebraic Multiplicity of Eigenvalues of Linear Operators

Name: Algebraic Multiplicity of Eigenvalues of Linear Operators
Brand: Birkhäuser Basel, Springer, Basel
SKU: 12720531
Price: 106.99 EUR
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Autoren: J. Lopez-Gomez , C. Mora-Corral

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Algebraic Multiplicity of Eigenvalues of Linear Operators, J. Lopez-Gomez, C. Mora-Corral

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Produktinformationen zu „Algebraic Multiplicity of Eigenvalues of Linear Operators “

This book brings together all available results about the theory of algebraic multiplicities. It first offers a classic course on finite-dimensional spectral theory and then presents the most general results available about the existence and uniqueness of algebraic multiplicities for real non-analytic operator matrices and families. Coverage next transfers these results from linear to nonlinear analysis.

Klappentext zu „Algebraic Multiplicity of Eigenvalues of Linear Operators “

This book analyzes the existence and uniqueness of a generalized algebraic m- tiplicity for a general one-parameter family L of bounded linear operators with Fredholm index zero at a value of the parameter ? whereL(? ) is non-invertible. 0 0 Precisely, given K?{R,C}, two Banach spaces U and V over K, an open subset ? ? K,andapoint ? ? ?, our admissible operator families are the maps 0 r L?C (? ,L(U,V)) (1) for some r? N, such that L(? )? Fred (U,V); 0 0 hereL(U,V) stands for the space of linear continuous operatorsfrom U to V,and Fred (U,V) is its subset consisting of all Fredholm operators of index zero. From 0 the point of view of its novelty, the main achievements of this book are reached in case K = R, since in the case K = C and r = 1, most of its contents are classic, except for the axiomatization theorem of the multiplicity.

Inhaltsverzeichnis zu „Algebraic Multiplicity of Eigenvalues of Linear Operators “

- Preface

I. Finite-dimensional Classic Spectral Theory

- The Jordan Theorem

- Operator Calculus

- Spectral Projections

II. Algebraic Multiplicities

- Transversalization, Polynomial Factorization, Uniqueness, Jordan Chains, Smith Form, Logarithmic Residues

- Analytic and Classical Families. Stability

- Spectral Theorem for Matrix Polynomials

- Further Developments

III. Nonlinear Spectral Theory

- Bibliography

- Index

Bibliographische Angaben

Autoren: J. Lopez-Gomez , C. Mora-Corral
2007, 2007, 310 Seiten, Maße: 17,4 x 24,2 cm, Gebunden, Deutsch
Verlag: Birkhäuser Basel
ISBN-10: 376438400X
ISBN-13: 9783764384005
Erscheinungsdatum: 28.08.2007

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