© 1992

Functional Analysis I

Linear Functional Analysis

  • N. K. Nikol’skij

Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 19)

Table of contents

  1. Front Matter
    Pages I-5
  2. Yu. I. Lyubich
    Pages 6-84
  3. Yu. I. Lyubich
    Pages 85-260
  4. Back Matter
    Pages 261-286

About this book


Up to a certain time the attention of mathematicians was concentrated on the study of individual objects, for example, specific elementary functions or curves defined by special equations. With the creation of the method of Fourier series, which allowed mathematicians to work with 'arbitrary' functions, the individual approach was replaced by the 'class' approach, in which a particular function is considered only as an element of some 'function space'. More or less simultane­ ously the development of geometry and algebra led to the general concept of a linear space, while in analysis the basic forms of convergence for series of functions were identified: uniform, mean square, pointwise and so on. It turns out, moreover, that a specific type of convergence is associated with each linear function space, for example, uniform convergence in the case of the space of continuous functions on a closed interval. It was only comparatively recently that in this connection the general idea of a linear topological space (L TS)l was formed; here the algebraic structure is compatible with the topological structure in the sense that the basic operations (addition and multiplication by a scalar) are continuous.


Anwendungen der Funktionalalysis Applications of Functional Analysis Linear Functional Analysis Lineare Funktionalanalysis Operator theory Topological Vector Spaces Topologischer Vektorraum calculus differential equation functional analysis

Authors and affiliations

  1. 1.Department of MathematicsState University of New York at Stony BrookStony BrookUSA

Editors and affiliations

  • N. K. Nikol’skij
    • 1
  1. 1.Steklov Mathematical InstituteSt. PeterburgUSSR

Bibliographic information

  • Book Title Functional Analysis I
  • Book Subtitle Linear Functional Analysis
  • Authors Yu.I. Lyubich
  • Editors N.K. Nikol'skij
  • Series Title Encyclopaedia of Mathematical Sciences
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1992
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-50584-6
  • Softcover ISBN 978-3-642-08070-8
  • eBook ISBN 978-3-662-02849-0
  • Series ISSN 0938-0396
  • Edition Number 1
  • Number of Pages V, 286
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Original Russian edition published by Publisher VINITI, Moscow, 1988
  • Topics Analysis
  • Buy this book on publisher's site
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