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130626 ||| eng |
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|a 9783764384012
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| 100 |
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|a López-Gómez, Julián
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| 245 |
0 |
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|a Algebraic Multiplicity of Eigenvalues of Linear Operators
|h Elektronische Ressource
|c by Julián López-Gómez, Carlos Mora-Corral
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| 250 |
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|a 1st ed. 2007
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| 260 |
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|a Basel
|b Birkhäuser
|c 2007, 2007
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| 300 |
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|a XXII, 310 p
|b online resource
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| 505 |
0 |
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|a 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
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| 653 |
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|a Functional analysis
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| 653 |
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|a Functional Analysis
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| 653 |
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|a Linear Algebra
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| 653 |
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|a Operator theory
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| 653 |
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|a Mathematical physics
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| 653 |
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|a Operator Theory
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| 653 |
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|a Algebras, Linear
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| 653 |
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|a Mathematical Methods in Physics
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| 700 |
1 |
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|a Mora-Corral, Carlos
|e [author]
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| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b Springer
|a Springer eBooks 2005-
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| 490 |
0 |
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|a Operator Theory: Advances and Applications
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| 028 |
5 |
0 |
|a 10.1007/978-3-7643-8401-2
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| 856 |
4 |
0 |
|u https://doi.org/10.1007/978-3-7643-8401-2?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
0 |
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|a 515.7
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| 520 |
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|a 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)
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