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Unbounded Linear Operators Theory and Applications~tqw~ darksiderg

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Unbounded Linear Operators: Theory and Applications
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Type.................: Ebook
Part Size............: 6,450,991 bytes

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Posted by............: ~tqw~

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Release Notes
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In recent years important progress has been made in the study of linear
operators by extending to closed operators many fundamental theorems
which were known for bounded operators. The applications of the
theory permit unification of a series of diverse questions in differential
equations, which leads to significant results with substantial simplification.

Table Of Contents

Preface v
Preliminaries 1
I INTRODUCTION TO NORMED LINEAR SPACES 4
1. Examples of normed linear spaces 4-
2. Complete normed linear spaces 6
3. Bounded linear operators 10
4. Finite-dimensional normed linear spaces 13
5. Hahn-Banach extension theorem 16
6. Conjugate spaces 24-
7. Hilbert spaces 31
II LINEAR OPERATORS AND THEIR CONJUGATES 42
1. Closed linear operators 43
2. Conjugate of a linear operator 49
3. States of linear operators 58
4. States of closed linear operators 62
5. Examples of states 66
6. Characterizations of states of operators 72
7. Adjoint of an operator in Hilbert space 74
III STRICTLY SINGULAR OPERATORS 76
1. Compact operators 76
2. Relationship between strictly singular and compact operators 83
3. Examples of noncompact, strictly singular operators 88
4· Conjugates of strictly singular operators 92
IV OPERATORS WITH CLOSED RANGE 94
1. Minimum moudlus of an operator 94
B. Index of a linear operator 101
V PERTURBATION THEORY
1. Perturbation by bounded operators
2. Perturbation by strictly singular operators
3. Perturbation by unbounded operators
VI APPLICATIONS TO ORDINARY DIFFERENTIAL OPERATORS 125
1. Conjugates and preconjugates of differential operators 126
2. Minimal and maximal operators 135
3. Maximal operators corresponding to compact intervals 140
4. Extension theorems 148
5. Boundary value functionals 153
6. Some a priori estimates 157
7. The constant coefficient and the Euler differential operators 162
8. Perturbations of the bounded coefficient and the Euler
operators 166
VII THE OIRICHLET OPERATOR 179
1. The Sobolev space Wm,p(n) 179
2. A priori estimates and differential operators 184
Bibliography 191
Index 197

Product Details

* ISBN: 0486453316
* ISBN-13: 9780486453316
* Format: Paperback, 208pp
* Publisher: Dover Publications
* Pub. Date: August 2006

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