Linear Equations in Banach Spaces

  • S. G. Krein

Table of contents

  1. Front Matter
    Pages I-1
  2. S. G. Krein
    Pages 3-5
  3. S. G. Krein
    Pages 6-9
  4. S. G. Krein
    Pages 10-16
  5. S. G. Krein
    Pages 24-26
  6. S. G. Krein
    Pages 27-29
  7. S. G. Krein
    Pages 30-32
  8. S. G. Krein
    Pages 33-37
  9. S. G. Krein
    Pages 38-41
  10. S. G. Krein
    Pages 42-43
  11. S. G. Krein
    Pages 50-52
  12. S. G. Krein
    Pages 59-61
  13. S. G. Krein
    Pages 62-64
  14. S. G. Krein
    Pages 65-79

About this book

Introduction

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.

Keywords

BASIC DEX Factor THE banach spaces differential equation form function functional analysis integral integral equation kernel operator university variable

Authors and affiliations

  • S. G. Krein
    • 1
  1. 1.Department of MathematicsVoronezh UniversityVoronezhUSSR

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-8068-9
  • Copyright Information Birkhäuser Boston 1982
  • Publisher Name Birkhäuser Boston
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-8176-3101-7
  • Online ISBN 978-1-4684-8068-9
  • About this book