Ebook: Algebraic Multiplicity of Eigenvalues of Linear Operators
- Genre: Mathematics // Algebra
- Tags: Functional Analysis, Linear and Multilinear Algebras Matrix Theory, Mathematical Methods in Physics, Operator Theory
- Series: Operator Theory: Advances and Applications 177
- Year: 2007
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
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).