MTU Cork Library Catalogue

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History of functional analysis / Jean Dieudonne.

By: Dieudonné, Jean, 1906-1992.
Material type: materialTypeLabelBookSeries: North-Holland mathematics studies ; 49.Notas de matemàtica (Rio de Janeiro, Brazil): Publisher: Amsterdam ; New York : New York : North-Holland Pub. Co., sole distributors for the U.S.A. and Canada, Elsevier/North-Holland, 1981Description: vi, 312 p. ; 24 cm. + pbk.ISBN: 0444861483 (Elsevier).Subject(s): Functional analysis -- HistoryDDC classification: 515.709
Contents:
Linear differential equations and the Strum-Liouville problem -- The "crypto-integral" equations -- The equation of vibrating membranes -- The idea of infinite dimension -- The crucial years and the definition of Hilbert space -- Duality and the definition of normed spaces -- Spectral theory after 1900 -- Locally convex spaces and the theory of distributions -- Applications of functional analysis to differential and partial differential equations.
Holdings
Item type Current library Call number Copy number Status Date due Barcode Item holds
General Lending MTU Bishopstown Library Lending 515.709 (Browse shelf(Opens below)) 1 Available 00023059
Total holds: 0

Enhanced descriptions from Syndetics:

History of Functional Analysis presents functional analysis as a rather complex blend of algebra and topology, with its evolution influenced by the development of these two branches of mathematics. The book adopts a narrower definition--one that is assumed to satisfy various algebraic and topological conditions. A moment of reflections shows that this already covers a large part of modern analysis, in particular, the theory of partial differential equations. This volume comprises nine chapters, the first of which focuses on linear differential equations and the Sturm-Liouville problem. The succeeding chapters go on to discuss the ""crypto-integral"" equations, including the Dirichlet principle and the Beer-Neumann method; the equation of vibrating membranes, including the contributions of Poincare and H.A. Schwarz's 1885 paper; and the idea of infinite dimension. Other chapters cover the crucial years and the definition of Hilbert space, including Fredholm's discovery and the contributions of Hilbert; duality and the definition of normed spaces, including the Hahn-Banach theorem and the method of the gliding hump and Baire category; spectral theory after 1900, including the theories and works of F. Riesz, Hilbert, von Neumann, Weyl, and Carleman; locally convex spaces and the theory of distributions; and applications of functional analysis to differential and partial differential equations. This book will be of interest to practitioners in the fields of mathematics and statistics.

Includes bibliographical references (pages 280-298) and indexes.

Linear differential equations and the Strum-Liouville problem -- The "crypto-integral" equations -- The equation of vibrating membranes -- The idea of infinite dimension -- The crucial years and the definition of Hilbert space -- Duality and the definition of normed spaces -- Spectral theory after 1900 -- Locally convex spaces and the theory of distributions -- Applications of functional analysis to differential and partial differential equations.

Table of contents provided by Syndetics

  • Linear Differential Equations and the Sturm-Liouville Problem
  • The "Crypto-Integral' Equations
  • The Equation of Vibrating Membranes
  • The Idea of Infinite Dimension
  • The Crucial Years and the Definition of Hilbert Space
  • Duality and the Definition of Normed Spaces
  • Spectral Theory after 1900
  • Locally Convex Spaces and the Theory of Distributions
  • Applications of Functional Analysis to Differential and Partial Differential Equations
  • References
  • Author and Subject Index

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