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基本説明
Brings together all available results about the theory of algebraic multiplicities, from the most classic results, like the Jordan Theorem, to the most recent developments, like the uniqueness theorem and the construction of the multiplicity for non-analytic families.
Full Description
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.
Contents
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.
