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Linear Equations in Banach Spaces

  • Book
  • © 1982

Overview

Authors:
  1. S. G. Krein

    1. Department of Mathematics, Voronezh University, Voronezh, USSR

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Table of contents (20 chapters)

  1. Front Matter

    Pages I-1
    Download chapter PDF

  2. Linear equations. Basic Notions

    • S. G. Krein
    Pages 3-5

  3. Equations with a Closed Operator

    • S. G. Krein
    Pages 6-9

  4. The Adjoint Equation

    • S. G. Krein
    Pages 10-16

  5. The Equation Adjoint to the Factored Equation

    • S. G. Krein
    Pages 17-17

  6. An Equation with a Closed Operator Which Has a Dense Domain

    • S. G. Krein
    Pages 18-21

  7. Normally Solvable Equations with Finite Dimensional Kernel

    • S. G. Krein
    Pages 22-23

  8. A Priori Estimates

    • S. G. Krein
    Pages 24-26

  9. Equations with Finite Defect

    • S. G. Krein
    Pages 27-29

  10. Some Different Adjoint Equations

    • S. G. Krein
    Pages 30-32

  11. Linear Transformations of Equations

    • S. G. Krein
    Pages 33-37

  12. Transformations of d-Normal Equations

    • S. G. Krein
    Pages 38-41

  13. Noetherian Equations. Index

    • S. G. Krein
    Pages 42-43

  14. Equations with Operators Which Act in a Single Space

    • S. G. Krein
    Pages 44-45

  15. Fredholm Equations. Regularization of Equations

    • S. G. Krein
    Pages 46-49

  16. Linear Changes of Variable

    • S. G. Krein
    Pages 50-52

  17. Stability of the Properties of an Equation

    • S. G. Krein
    Pages 53-58

  18. Overdetermined Equations

    • S. G. Krein
    Pages 59-61

  19. Undetermined Equations

    • S. G. Krein
    Pages 62-64

  20. Integral Equations

    • S. G. Krein
    Pages 65-79
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Keywords

About this book

INTRODUCTION . . . . . . xiii § 1. LINEAR EQUATIONS. BASIC NOTIONS . 3 § 2. EQUATIONS WITH A CLOSED OPERATOR 6 § 3. THE ADJOINT EQUATION . . . . . . 10 § 4. THE EQUATION ADJOINT TO THE FACTORED EQUATION. 17 § 5. AN EQUATION WITH A CLOSED OPERATOR WHICH HAS A DENSE DOMAIN 18 NORMALLY SOLVABLE EQUATIONS WITH FINITE DIMENSIONAL KERNEL. 22 § 6. A PRIORI ESTIMATES .. . . . . . 24 § 7. EQUATIONS WITH FINITE DEFECT . . . 27 § 8. § 9. SOME DIFFERENT ADJOINT EQUATIONS . 30 § 10. LINEAR TRANSFORMATIONS OF EQUATIONS 33 TRANSFORMATIONS OF d-NORMAL EQUATIONS . 38 § 11. § 12. NOETHERIAN EQUATIONS. INDEX. . . . . . 42 § 13. EQUATIONS WITH OPERATORS WHICH ACT IN A SINGLE SPACE 44 § 14. FREDHOLM EQUATIONS. REGULARIZATION OF EQUATIONS 46 § 15. LINEAR CHANGES OF VARIABLE . . . . . . . . 50 § 16. STABILITY OF THE PROPERTIES OF AN EQUATION 53 OVERDETERMINED EQUATIONS 59 § 17. § 18. UNDETERMINED EQUATIONS 62 § 19. INTEGRAL EQUATIONS . . . 65 DIFFERENTIAL EQUATIONS . 80 § 20. APPENDIX. BASIC RESULTS FROM FUNCTIONAL ANALYSIS USED IN THE TEXT 95 LITERATURE CITED . . . . . . . . . . . . . . . . . . .. . . . 99 . . PRE F ACE The basic material appearing in this book represents the substance v of a special series of lectures given by the author at Voronez University in 1968/69, and, in part, at Dagestan University in 1970.

Authors and Affiliations

  • Department of Mathematics, Voronezh University, Voronezh, USSR

    S. G. Krein

Bibliographic Information

  • Book Title: Linear Equations in Banach Spaces

  • Authors: S. G. Krein

  • DOI: https://doi.org/10.1007/978-1-4684-8068-9

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1982

  • Softcover ISBN: 978-0-8176-3101-7Published: 01 January 1982

  • eBook ISBN: 978-1-4684-8068-9Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XII, 106

  • Topics: Functional Analysis, Topology

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