Linear Equations in Banach Spaces

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.