rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Algebraic Multiplicity of Eigenvalues of Linear Operators
  name:
    name part: López-Gómez, J.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Mora-Corral, C.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: sz
    date issued: 2007
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXII, 310 p. online resource.
  abstract: 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).
  table of 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.
  note: by J. López-Gómez, C. Mora-Corral.
  subject:
    topic: Mathematics
  subject:
    topic: Matrix theory
  subject:
    topic: Algebra
  subject:
    topic: Functional analysis
  subject:
    topic: Operator theory
  subject:
    topic: Physics
  subject:
    topic: Mathematics
  subject:
    topic: Functional Analysis
  subject:
    topic: Linear and Multilinear Algebras, Matrix Theory
  subject:
    topic: Mathematical Methods in Physics
  subject:
    topic: Operator Theory
  classification: QA319-329.9
  classification: 515.7
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Operator Theory: Advances and Applications ; 177
  identifier: 9783764384012
  identifier: http://dx.doi.org/10.1007/978-3-7643-8401-2
  record info:
    record creation date: 100301
    record change date: 20151204170435.0
    record identifier: 978-3-7643-8401-2