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: Fourier Analysis on Finite Abelian Groups
  name:
    name part: Luong, Bao.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2009
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVI, 159 p. online resource.
  abstract: Fourier analysis has been the inspiration for a technological wave of advances in fields such as imaging processing, financial modeling, cryptography, algorithms, and sequence design. This self-contained book provides a thorough look at the Fourier transform, one of the most useful tools in applied mathematics. With countless examples and unique exercise sets at the end of most sections, Fourier Analysis on Finite Abelian Groups is a perfect companion for a first course in Fourier analysis. The first two chapters provide fundamental material for a strong foundation to deal with subsequent chapters. Special topics covered include: * Computing eigenvalues of the Fourier transform * Applications to Banach algebras * Tensor decompositions of the Fourier transform * Quadratic Gaussian sums This book provides a useful introduction for well-prepared undergraduate and graduate students and powerful applications that may appeal to researchers and mathematicians. The only prerequisites are courses in group theory and linear algebra.
  table of contents: Preface -- Overview -- Chapter 1: Foundation Material -- Results from Group Theory -- Quadratic Congruences -- Chebyshev Systems of Functions -- Chapter 2: The Fourier Transform -- A Special Class of Linear Operators -- Characters -- The Orthogonal Relations for Characters -- The Fourier Transform -- The Fourier Transform of Periodic Functions -- The Inverse Fourier Transform -- The Inversion Formula -- Matrices of the Fourier Transform -- Iterated Fourier Transform -- Is the Fourier Transform a Self-Adjoint Operator? -- The Convolutions Operator -- Banach Algebra -- The Uncertainty Principle -- The Tensor Decomposition -- The Tensor Decomposition of Vector Spaces -- The Fourier Transform and Isometries -- Reduction to Finite Cyclic Groups -- Symmetric and Antisymmetric Functions -- Eigenvalues and Eigenvectors -- Spectrak Theorem -- Ergodic Theorem -- Multiplicities of Eigenvalues -- The Quantum Fourier Transform -- Chapter 3: Quadratic Sums -- 1. The Number G_n(1) -- Reduction Formulas.
  note: by Bao Luong.
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Group theory
  subject:
    topic: Mathematical analysis
  subject:
    topic: Analysis (Mathematics)
  subject:
    topic: Fourier analysis
  subject:
    topic: Mathematics
  subject:
    topic: Analysis
  subject:
    topic: Algebra
  subject:
    topic: Fourier Analysis
  subject:
    topic: Group Theory and Generalizations
  classification: QA299.6-433
  classification: 515
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Applied and Numerical Harmonic Analysis
  identifier: 9780817649166
  identifier: http://dx.doi.org/10.1007/978-0-8176-4916-6
  record info:
    record creation date: 100715
    record change date: 20151204185138.0
    record identifier: 978-0-8176-4916-6