Krein

Linear Equations in Banach Spaces (eBook, PDF)

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Birkhäuser Boston
• Seitenzahl: 106
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781468480689
• Artikelnr.: 44209405

Inhaltsangabe

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.