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Functional Analysis I

Linear Functional Analysis

  • Book
  • © 1992

Overview

Authors:
  1. Yu. I. Lyubich

    1. Department of Mathematics, State University of New York at Stony Brook, Stony Brook, USA

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Editors:
  1. N. K. Nikol’skij

    1. Steklov Mathematical Institute, St. Peterburg, USSR

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

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Table of contents (2 chapters)

  1. Front Matter

    Pages I-5
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  2. Classical Concrete Problems

    • Yu. I. Lyubich
    Pages 6-84

  3. Foundations and Methods

    • Yu. I. Lyubich
    Pages 85-260

  4. Back Matter

    Pages 261-286
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Keywords

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.

Authors, Editors and Affiliations

  • Steklov Mathematical Institute, St. Peterburg, USSR

    N. K. Nikol’skij

  • Department of Mathematics, State University of New York at Stony Brook, Stony Brook, USA

    Yu. I. Lyubich

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: https://doi.org/10.1007/978-3-662-02849-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1992

  • Hardcover ISBN: 978-3-540-50584-6Published: 06 February 1992

  • Softcover ISBN: 978-3-642-08070-8Published: 01 December 2010

  • eBook ISBN: 978-3-662-02849-0Published: 09 March 2013

  • Series ISSN: 0938-0396

  • Edition Number: 1

  • Number of Pages: V, 286

  • Additional Information: Original Russian edition published by Publisher VINITI, Moscow, 1988

  • Topics: Analysis

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