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＜電子ブック＞
Algebraic Multiplicity of Eigenvalues of Linear Operators / by Julián López-Gómez, Carlos Mora-Corral
(Operator Theory: Advances and Applications. ISSN:22964878 ; 177)

版	1st ed. 2007.
出版者	(Basel : Birkhäuser Basel : Imprint: Birkhäuser)
出版年	2007
本文言語	英語
大きさ	XXII, 310 p : online resource
著者標目	*López-Gómez, Julián author Mora-Corral, Carlos author SpringerLink (Online service)
件　名	LCSH:Functional analysis LCSH:Algebras, Linear LCSH:Mathematical physics LCSH:Operator theory FREE:Functional Analysis FREE:Linear Algebra FREE:Mathematical Methods in Physics FREE:Operator Theory
一般注記	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 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) HTTP:URL=https://doi.org/10.1007/978-3-7643-8401-2

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