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 and approximation of functions
  name:
    name part: Trigub, Roald M.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Belinsky, Eduard S.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: ne
    date issued: 2004
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (xiii, 585 pages)
  abstract: In Fourier Analysis and Approximation of Functions basics of classical Fourier Analysis are given as well as those of approximation by polynomials, splines and entire functions of exponential type. In Chapter 1 which has an introductory nature, theorems on convergence, in that or another sense, of integral operators are given. In Chapter 2 basic properties of simple and multiple Fourier series are discussed, while in Chapter 3 those of Fourier integrals are studied. The first three chapters as well as partially Chapter 4 and classical Wiener, Bochner, Bernstein, Khintchin, and Beurling theorems in Chapter 6 might be interesting and available to all familiar with fundamentals of integration theory and elements of Complex Analysis and Operator Theory. Applied mathematicians interested in harmonic analysis and/or numerical methods based on ideas of Approximation Theory are among them. In Chapters 6-11 very recent results are sometimes given in certain directions. Many of these results have never appeared as a book or certain consistent part of a book and can be found only in periodics; looking for them in numerous journals might be quite onerous, thus this book may work as a reference source. The methods used in the book are those of classical analysis, Fourier Analysis in finite-dimensional Euclidean space Diophantine Analysis, and random choice.
  table of contents: 1. Representation Theorems -- 1.1 Theorems on representation at a point -- 1.2 Integral operators. Convergence in Lp-norm and almost everywhere -- 1.3 Multidimensional case -- 1.4 Further problems and theorems -- 1.5 Comments to Chapter 1 -- 2. Fourier Series -- 2.1 Convergence and divergence -- 2.2 Two classical summability methods -- 2.3 Harmonic functions and functions analytic in the disk -- 2.4 Multidimensional case -- 2.5 Further problems and theorems -- 2.6 Comments to Chapter 2 -- 3. Fourier Integral -- 3.1 L-Theory -- 3.2 L2-Theory -- 3.3 Multidimensional case -- 3.4 Entire functions of exponential type. The Paley-Wiener theorem -- 3.5 Further problems and theorems -- 3.6 Comments to Chapter 3 -- 4. Discretization. Direct and Inverse Theorems -- 4.1 Summation formulas of Poisson and Euler-Maclaurin -- 4.2 Entire functions of exponential type and polynomials -- 4.3 Network norms. Inequalities of different metrics -- 4.4 Direct theorems of Approximation Theory -- 4.5 Inverse theorems. Constructive characteristics. Embedding theorems -- 4.6 Moduli of smoothness -- 4.7 Approximation on an interval -- 4.8 Further problems and theorems -- 4.9 Comments to Chapter 4 -- 5. Extremal Problems of Approximation Theory -- 5.1 Best approximation -- 5.2 The space Lp. Best approximation -- 5.3 Space C. The Chebyshev alternation -- 5.4 Extremal properties for algebraic polynomials and splines -- 5.5 Best approximation of a set by another set -- 5.6 Further problems and theorems -- 5.7 Comments to Chapter 5 -- 6. A Function as the Fourier Transform of A Measure -- 6.1 Algebras A and B. The Wiener Tauberian theorem -- 6.2 Positive definite and completely monotone functions -- 6.3 Positive definite functions depending only on a norm -- 6.4 Sufficient conditions for belonging to Ap and A* -- 6.5 Further problems and theorems -- 6.6 Comments to Chapter 6 -- 7. Fourier Multipliers -- 7.1 General properties -- 7.2 Sufficient conditions -- 7.3 Multipliers of power series in the Hard…
  note: by Roald M. Trigub and Eduard S. Bellinsky.
  note: Originally published: Dordrecht; London: Kluwer Academic Publishers, 2004.
  note: "Softcover reprint of the hardcover 1st edition 2004"--Title page verso.
  note: Includes bibliographical references and index.
  subject:
    topic: Fourier analysis
  subject:
    topic: Approximation theory
  subject:
    topic: Functions
  subject:
    topic: Approximation theory
  subject:
    topic: Fourier analysis
  subject:
    topic: Functions
  classification: QA403.5
  classification: 515.2433
  related item:
    title info:
      title: Fourier analysis and approximation of functions
    name:
      name part: Trigub, Roald M.
    identifier: (OCoLC)751543375
  identifier: 9781402023422 (electronic bk.)
  identifier: 1402023421 (electronic bk.)
  identifier: 9781402028762 (electronic bk.)
  identifier: 1402028768 (electronic bk.)
  identifier: 9789048166411
  identifier: 9048166411
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: GW5XE
    record creation date: 140826
    record change date: 20260422224730.1
    record identifier: in00003538534
    language of cataloging:
      language term: eng