Algebraic Multiplicity of Eigenvalues of Linear Operators
Seiten
2007
|
2007
Springer Basel (Verlag)
978-3-7643-8400-5 (ISBN)
Springer Basel (Verlag)
978-3-7643-8400-5 (ISBN)
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 |
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