Linear Equations in Banach Spaces [Paperback]

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.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. FREDHl3^