INTRODUCTION . . . . . . xiii ยง 1. LINEAR EQUATIONS. BASIC NOTIONS . 3 ยง 2. EQUATIONS WITH A CLOSED OPERATOR 6 ยง 3. THE ADJOINT EQUATION . . . . . . 10 ยง 4. THE EQUATION ADJOINT TO THE FACTORED EQUATION. 17 ยง 5. AN EQUATION WITH A CLOSED OPERATOR WHICH HAS A DENSE DOMAIN 18 NORMALLY SOLVABLE EQUATIONS WITH FINITE DIMENSIONAL KERNEL. 22 ยง 6. A PRIORI ESTIMATES .. . . . . . 24 ยง 7. EQUATIONS WITH FINITE DEFECT . . . 27 ยง 8. ยง 9. SOME DIFFERENT ADJOINT EQUATIONS . 30 ยง 10. LINEAR TRANSFORMATIONS OF EQUATIONS 33 TRANSFORMATIONS OF d-NORMAL EQUATIONS . 38 ยง 11. ยง 12. NOETHERIAN EQUATIONS. INDEX. . . . . . 42 ยง 13. EQUATIONS WITH OPERATORS WHICH ACT IN A SINGLE SPACE 44 ยง 14. FREDHOLM EQUATIONS. REGULARIZATION OF EQUATIONS 46 ยง 15. LINEAR CHANGES OF VARIABLE . . . . . . . . 50 ยง 16. STABILITY OF THE PROPERTIES OF AN EQUATION 53 OVERDETERMINED EQUATIONS 59 ยง 17. ยง 18. UNDETERMINED EQUATIONS 62 ยง 19. INTEGRAL EQUATIONS . . . 65 DIFFERENTIAL EQUATIONS . 80 ยง 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
CONTENT
ยง 1. Linear equations. Basic notions -- ยง 2. Equations with a Closed Operator -- ยง 3. The Adjoint Equation -- ยง 4. The Equation Adjoint to the Factored Equation -- ยง 5. An Equation with a Closed Operator Which Has a Dense Domain -- ยง 6. Normally Solvable Equations with Finite Dimensional Kernel -- ยง 7. A Priori Estimates -- ยง 8. Equations with Finite Defect -- ยง 9. Some Different Adjoint Equations -- ยง 10. Linear Transformations of Equations -- ยง11. Transformations of d-Normal Equations -- ยง 12. Noetherian equations. Index -- ยง 13. Equations with Operators Which Act in a Single Space -- ยง 14. Fredholm equations. Regularization of equations -- ยง 15. Linear Changes of Variable -- ยง 16. Stability of the Properties of an Equation -- ยง 17. Overdetermined Equations -- ยง 18. Undetermined Equations -- ยง 19. Integral Equations -- ยง 20. Differential Equations -- Appendix. Basic results from functional analysis used in the text -- Literature cited
