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 ...
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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.
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