Julián López-Gómez, Carlos Mora-Corral

Algebraic Multiplicity of Eigenvalues of Linear Operators (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book brings together all the most important known results of research into the theory of algebraic multiplicities, from well-known classics like the Jordan Theorem to recent developments such as the uniqueness theorem and the construction of multiplicity for non-analytic families, which is presented in this monograph for the first time.

Part I (the first three chapters) is a classic course on finite-dimensional spectral theory; Part II (the next eight chapters) contains the most general results available about the existence and uniqueness of algebraic multiplicities for real non-analytic operator matrices and families; and Part III (the last chapter) transfers these results from linear to nonlinear analysis.

The text is as self-contained as possible. All the results are established in a finite-dimensional setting, if necessary. Furthermore, the structure and style of the book make it easy to access some of the most important and recent developments. Thus the material appeals to a broad audience, ranging from advanced undergraduates (in particular Part I) to graduates, postgraduates and reseachers who will enjoy the latest developments in the real non-analytic case (Part II).

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Produktdetails

• Verlag: Birkhäuser Basel
• Seitenzahl: 310
• Erscheinungstermin: 9. August 2007
• Englisch
• ISBN-13: 9783764384012
• Artikelnr.: 37397789

Autorenporträt

Julián López-Gómez, Universidad Complutense de Madrid, Spain / Carlos Mora-Corral, University of Oxford, UK

Inhaltsangabe

Finite-dimensional Classic Spectral Theory.- The Jordan Theorem.- Operator Calculus.- Spectral Projections.- Algebraic Multiplicities.- Algebraic Multiplicity Through Transversalization.- Algebraic Multiplicity Through Polynomial Factorization.- Uniqueness of the Algebraic Multiplicity.- Algebraic Multiplicity Through Jordan Chains. Smith Form.- Analytic and Classical Families. Stability.- Algebraic Multiplicity Through Logarithmic Residues.- The Spectral Theorem for Matrix Polynomials.- Further Developments of the Algebraic Multiplicity.- Nonlinear Spectral Theory.- Nonlinear Eigenvalues.