TY  - BOOK
AU  - López-Gómez,J.
AU  - Mora-Corral,C.
ED  - SpringerLink (Online service)
TI  - Algebraic Multiplicity of Eigenvalues of Linear Operators
T2  - Operator Theory: Advances and Applications,
SN  - 9783764384012
AV  - QA319-329.9 
U1  - 515.7 23
PY  - 2007///
CY  - Basel
PB  - Birkhäuser Basel
KW  - Functional analysis
KW  - Matrix theory
KW  - Mathematical physics
KW  - Operator theory
KW  - Functional Analysis
KW  - Linear and Multilinear Algebras, Matrix Theory
KW  - Mathematical Methods in Physics
KW  - Operator Theory
N1  - 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
N2  - 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)
UR  - https://doi.org/10.1007/978-3-7643-8401-2
ER  -