Linear Equations in Banach Spaces
Birkhauser Boston Inc (Verlag)
978-0-8176-3101-7 (ISBN)
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.
§ 1. Linear equations. Basic notions.- § 2. Equations with a Closed Operator.- § 3. The Adjoint Equation.- § 4. The Equation Adjoint to the Factored Equation.- § 5. An Equation with a Closed Operator Which Has a Dense Domain.- § 6. Normally Solvable Equations with Finite Dimensional Kernel.- § 7. A Priori Estimates.- § 8. Equations with Finite Defect.- § 9. Some Different Adjoint Equations.- § 10. Linear Transformations of Equations.- §11. Transformations of d-Normal Equations.- § 12. Noetherian equations. Index.- § 13. Equations with Operators Which Act in a Single Space.- § 14. Fredholm equations. Regularization of equations.- § 15. Linear Changes of Variable.- § 16. Stability of the Properties of an Equation.- § 17. Overdetermined Equations.- § 18. Undetermined Equations.- § 19. Integral Equations.- § 20. Differential Equations.- Appendix. Basic results from functional analysis used in the text.- Literature cited.
| Erscheint lt. Verlag | 1.1.1982 |
|---|---|
| Zusatzinfo | XII, 106 p. |
| Verlagsort | Secaucus |
| Sprache | englisch |
| Maße | 152 x 229 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 0-8176-3101-1 / 0817631011 |
| ISBN-13 | 978-0-8176-3101-7 / 9780817631017 |
| Zustand | Neuware |
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