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: Linear Functional Analysis
  name:
    name part: Rynne, Bryan Patrick.
    role:
      role term: creator
  name:
    name part: Youngson, Martin Alexander.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: enk
    date issued: 2000
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: access
    form: remote
    extent: 1 online resource (x, 273 pages)
  abstract: This introduction to the ideas and methods of linear functional analysis shows how familiar and useful concepts from finite-dimensional linear algebra can be extended or generalized to infinite-dimensional spaces. Aimed at advanced undergraduates in mathematics and physics, the book assumes a standard background of linear algebra, real analysis (including the theory of metric spaces), and Lebesgue integration, although an introductory chapter summarizes the requisite material. The initial chapters develop the theory of infinite-dimensional normed spaces, in particular Hilbert spaces, after which the emphasis shifts to studying operators between such spaces. Functional analysis has applications to a vast range of areas of mathematics; the final chapters discuss the particularly important areas of integral and differential equations. Further highlights of the second edition include: a new chapter on the Hahn-Banach theorem and its applications to the theory of duality. This chapter also introduces the basic properties of projection operators on Banach spaces, and weak convergence of sequences in Banach spaces - topics that have applications to both linear and nonlinear functional analysis; extended coverage of the uniform boundedness theorem; plenty of exercises, with solutions provided at the back of the book. Praise for the first edition: "The authors write with a strong narrative thrust and a sensitive appreciation of the needs of the average student so that, by the final chapter, there is a real feeling of having 'gotten somewhere worth getting' by a sensibly paced, clearly signposted route." Mathematical Gazette "It is a fine book, with material well-organized and well-presented. A particularly useful feature is the material on compact operators and applications to differential equations." CHOICE.
  table of contents: Preliminaries -- Normed Spaces -- Inner Product Spaces, Hilbert Spaces -- Linear Operators -- Duality and the Hahn-Banach Theorem -- Linear Operators on Hilbert Spaces -- Compact Operators -- Integral and Differential Equations -- Solutions to Exercises -- Further Reading -- References -- Notation Index -- Index.
  note: by Bryan Patrick Rynne, Martin Alexander Youngson.
  note: Electronic resource.
  subject:
    topic: Mathematics
  subject:
    topic: Global analysis (Mathematics)
  subject:
    topic: Global analysis (Mathematics)
  subject:
    topic: Mathematics
  classification: QA299.6-433
  classification: 515
  related item:
    title info:
      title: Springer undergraduate mathematics series
  identifier: 9781447136552 (electronic bk.)
  identifier: 1447136551 (electronic bk.)
  identifier: 9781852332570
  identifier: 1852332573
  identifier: 1447136551
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: AU@
    record creation date: 130202
    record change date: 20260422170436.1
    record identifier: in00003570718
    language of cataloging:
      language term: eng