Linear Equations in Banach Spaces

Description

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. Front Matter....Pages I-1 Linear equations. Basic Notions....Pages 3-5 Equations with a Closed Operator....Pages 6-9 The Adjoint Equation....Pages 10-16 The Equation Adjoint to the Factored Equation....Pages 17-17 An Equation with a Closed Operator Which Has a Dense Domain....Pages 18-21 Normally Solvable Equations with Finite Dimensional Kernel....Pages 22-23 A Priori Estimates....Pages 24-26 Equations with Finite Defect....Pages 27-29 Some Different Adjoint Equations....Pages 30-32 Linear Transformations of Equations....Pages 33-37 Transformations of d-Normal Equations....Pages 38-41 Noetherian Equations. Index....Pages 42-43 Equations with Operators Which Act in a Single Space....Pages 44-45 Fredholm Equations. Regularization of Equations....Pages 46-49 Linear Changes of Variable....Pages 50-52 Stability of the Properties of an Equation....Pages 53-58 Overdetermined Equations....Pages 59-61 Undetermined Equations....Pages 62-64 Integral Equations....Pages 65-79 Differential Equations....Pages 80-93 Back Matter....Pages 95-105