دانلود کتاب Linear Equations in Banach Spaces

This slim volume contains a general theory of linear
equations in Banach spaces with applications to differential
and integral equations. It contains a detailed analysis of
the uniqueness and correctness problem
of over-determined
and under-determined equations, connections between the
equation and its conjugate. Different transformations of
linear equations are considered. Some sections deal with
problems of stability and apriori estimates. Different
classes of equations, such as Fredholm equations, Noether
equations
and others are considered. Applications are given
to Fredholm integral equations, Volterra integral equations,
boundary problems for linear differential equations of
hiaher orders
and boundary problems for elliptic partial
differential equations.
To understand the book it is enou
h to have a limited
knowledqe of the basics of functional analysis. An appendix
at the end of the book contains the statements of the
theorems of functional analysis which are used in the main
text, and this will be found useful to the reader.
This book differs from others in its conciseness. It
keeps its aim clearly in sight and does not stray from that
aim; it is systematic and not difficult to read. It is
uncanny how much material the author was able to include ln
this slim volume.
The author is an outstanding expert in differential
equations, the theory of linear operators and applied
mathematics. This fact influences the choice of material,
the presentation and terminology. One clearly feels the
applied motives in the book.
The book may be recommended for senior underqraduate
students and graduates in mathematics and related fields.
In my opinion it is of interest to anybody dealinq with
linear equations.

Contents:

PREFACE . . . . . .


INTRODUCTION . . . . . .



1. LINEAR EQUAT
ONS. 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 . . . . . . . . . . . . . . . . . . . . . . . . .