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Functional Analysis

Applications in Mechanics and Inverse Problems

  • Book
  • © 2002

Overview

Authors:
  1. L. P. Lebedev

    1. Department of Mechanics and Mathematics, Rostov State University, Russia
      Department of Mathematics and Statistics, National University of Bogota, Colombia

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  2. I. I. Vorovich

    1. Department of Mechanics and Mathematics, Rostov State University, Russia

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  3. G. M. L. Gladwell

    1. Department of Civil Engineering, University of Waterloo, Canada

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Part of the book series: Solid Mechanics and Its Applications (SMIA, volume 100)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    Pages 1-18

  3. Introduction to Metric Spaces

    Pages 19-63

  4. Energy Spaces and Generalized Solutions

    Pages 65-98

  5. Approximation in a Normed Linear Space

    Pages 99-139

  6. Elements of the Theory of Linear Operators

    Pages 141-166

  7. Compactness and Its Consequences

    Pages 167-193

  8. Spectral Theory of Linear Operators

    Pages 195-218

  9. Applications to Inverse Problems

    Pages 219-239

  10. Back Matter

    Pages 241-253
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Keywords

About this book

This book started its life as a series of lectures given by the second author from the 1970’s onwards to students in their third and fourth years in the Department of Mechanics and Mathematics at Rostov State University. For these lectures there was also an audience of engineers and applied mechanicists who wished to understand the functional analysis used in contemporary research in their fields. These people were not so much interested in functional analysis itself as in its applications; they did not want to be told about functional analysis in its most abstract form, but wanted a guided tour through those parts of the analysis needed for their applications. The lecture notes evolved over the years as the first author started to make more formal typewritten versions incorporating new material. About 1990 the first author prepared an English version and submitted it to Kluwer Academic Publishers for inclusion in the series Solid Mechanics and its Applications. At that state the notes were divided into three long chapters covering linear and nonlinear analysis. As Series Editor, the third author started to edit them. The requirements of lecture notes and books are vastly different. A book has to be complete (in some sense), self contained, and able to be read without the help of an instructor.

Authors and Affiliations

  • Department of Mechanics and Mathematics, Rostov State University, Russia

    L. P. Lebedev, I. I. Vorovich

  • Department of Mathematics and Statistics, National University of Bogota, Colombia

    L. P. Lebedev

  • Department of Civil Engineering, University of Waterloo, Canada

    G. M. L. Gladwell

Bibliographic Information

  • Book Title: Functional Analysis

  • Book Subtitle: Applications in Mechanics and Inverse Problems

  • Authors: L. P. Lebedev, I. I. Vorovich, G. M. L. Gladwell

  • Series Title: Solid Mechanics and Its Applications

  • DOI: https://doi.org/10.1007/0-306-48397-1

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media B.V. 2002

  • Hardcover ISBN: 978-1-4020-0667-8Published: 30 June 2002

  • Softcover ISBN: 978-1-4020-0756-9Published: 30 June 2002

  • eBook ISBN: 978-0-306-48397-4Published: 29 April 2006

  • Series ISSN: 0925-0042

  • Series E-ISSN: 2214-7764

  • Edition Number: 2

  • Number of Pages: X, 254

  • Topics: Functional Analysis, Solid Mechanics, Partial Differential Equations, Civil Engineering, Analysis

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