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Algebraic Multiplicity of Eigenvalues of Linear Operators

Julián López-Gómez, Carlos Mora-Corral (Autoren)

Buch | Hardcover

XXII, 310 Seiten

2007 | 2007
Springer Basel (Verlag)
978-3-7643-8400-5 (ISBN)

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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.

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.

Erscheint lt. Verlag	22.6.2007
Reihe/Serie	Operator Theory: Advances and Applications
Zusatzinfo	XXII, 310 p.
Verlagsort	Basel
Sprache	englisch
Maße	170 x 244 mm
Gewicht	760 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Analysis
	Naturwissenschaften ► Physik / Astronomie
Schlagworte	algebraic multiplicity • eigenvalue • Eigenwert • Hardcover, Softcover / Mathematik/Analysis • HC/Mathematik/Analysis • Lineare Algebra • Matrix • matrix theory • spectral theory
ISBN-10	3-7643-8400-X / 376438400X
ISBN-13	978-3-7643-8400-5 / 9783764384005
Zustand	Neuware