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: From Euclidean to Hilbert spaces
    sub title: introduction to functional analysis and its applications
  name:
    name part: Provenzi, Edoardo.
    role:
      role term: creator
  type of resource: text
  genre: bibliography
  origin info:
    place:
      place term: enk
    place:
      place term: London
    place:
      place term: Hoboken
    publisher: ISTE Ltd.
    publisher: Wiley
    date issued: 2021
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource
  abstract: From Euclidian to Hilbert Spaces analyzes the transition from finite dimensional Euclidian spaces to infinite-dimensional Hilbert spaces, a notion that can sometimes be difficult for non-specialists to grasp. The focus is on the parallels and differences between the properties of the finite and infinite dimensions, noting the fundamental importance of coherence between the algebraic and topological structure, which makes Hilbert spaces the infinite-dimensional objects most closely related to Euclidian spaces. The common thread of this book is the Fourier transform, which is examined starting from the discrete Fourier transform (DFT), along with its applications in signal and image processing, passing through the Fourier series and finishing with the use of the Fourier transform to solve differential equations. The geometric structure of Hilbert spaces and the most significant properties of bounded linear operators in these spaces are also covered extensively. The theorems are presented with detailed proofs as well as meticulously explained exercises and solutions, with the aim of illustrating the variety of applications of the theoretical results.
  table of contents: Inner Product Spaces (Pre-Hilbert) -- The Discrete Fourier Transform and its Applications to Signal and Image Processing -- Lebesgue's Measure and Integration Theory -- Banach Spaces and Hilbert Spaces -- The Geometric Structure of Hilbert Spaces -- Bounded Linear Operators in Hilbert Spaces -- Quotient Space -- The Transpose (or Dual)of a Linear Operator -- Uniform, Strong and Weak Convergence.
  note: Edoardo Provenzi.
  note: Includes bibliographical references and index.
  subject:
    topic: Functional analysis
  classification: QA320 .P76 2021
  classification: 515.7
  related item:
    title info:
      title: From Euclidean to Hilbert spaces
    name:
      name part: Provenzi, Edoardo.
    origin info:
      publisher: London : ISTE Ltd. ; Hoboken : Wiley, 2021
  identifier: 9781119851318
  identifier: 1119851319
  identifier: 9781119851301
  identifier: 1119851300
  identifier: 1786306824
  identifier: 9781786306821
  identifier: 9781119851301 Wiley
  identifier: 9781786306821 O'Reilly Media
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: NhCcYBP
    record creation date: 210807
    record change date: 20260214204400.8
    record identifier: in00004688193
    language of cataloging:
      language term: eng