EBN EL NEAL
Well-Known Member
Theory of Linear Operators in Hilbert Space
By N. I. Akhiezer, I. M. Glazman
links
http://xinio.info/?http://ifile.it/zhey4a/0486677486.zip
password: ebooksclub.org
or
http://xinio.info/?http://ifile.it/4h7wazy/35225.rar
RAR archive password: twilightzone
or
http://xinio.info/?http://ifile.it/xb86znd/akhiezer_glazman.djvu
or
http://rapidshare.com/files/49544903/t01823.rar
RAR archive password: gigapedia.org"
or
http://rapidshare.com/files/2876492/Theory.Linear.Operators.Hilbert.Space-0486677486.rar
all of
type
djvu
(inlove)(inlove)(inlove)
Basic Operator Theory
By Israel Gohberg, Seymour Goldberg
By N. I. Akhiezer, I. M. Glazman
links
http://xinio.info/?http://ifile.it/zhey4a/0486677486.zip
password: ebooksclub.org
or
http://xinio.info/?http://ifile.it/4h7wazy/35225.rar
RAR archive password: twilightzone
or
http://xinio.info/?http://ifile.it/xb86znd/akhiezer_glazman.djvu
or
http://rapidshare.com/files/49544903/t01823.rar
RAR archive password: gigapedia.org"
or
http://rapidshare.com/files/2876492/Theory.Linear.Operators.Hilbert.Space-0486677486.rar
all of
type
djvu
(inlove)(inlove)(inlove)
Basic Operator Theory
By Israel Gohberg, Seymour Goldberg
TABLE OF CONTENTS
INTRODUCTION xi
CHAPTER I. HILBERT SPACES 1
1. Complex n-space 1
2. The Hilbert space I2 3
3. Definition of Hilbert space and its elementary properties 5
4. Distance from a point to a finite dimensional subspace 10
5. The Gram determinant 12
6. Incompatible systems of equations 16
7. Least squares fit 17
8. Distance to a convex set and projections onto subspaces 19
9. Orthonormal systems 21
10. Legendre polynomials 22
11. Orthonormal Bases 25
12. Fourier series 28
13. Completeness of the Legendre polynomials 30
14. Bases for the Hilbert space of functions on a square 31
15. Stability of orthonormal bases 33
16. Separable spaces 34
17. Equivalence of Hilbert spaces 36
18. Example of a non separable space 37
EXERCISES I 38
CHAPTER II. BOUNDED LINEAR OPERATORS ON HILBERT SPACES 51
1. Properties of bounded linear operators 51
2. Examples of bounded linear operators with estimates of norms 53
3. Continuity of a linear operator 57
4. Matrix representations of bounded linear operators 58
5. Bounded linear functionals 60
6. Operators of finite rank 63
7. Invertible operators 65
8. Inversion of operators by the iterative method 70
9. Infinite systems of linear equations 72
10. Integral equations of the second kind 74
11. Adjoint operators 77
12. Self adjoint operators 80
13. Orthogonal projections 82
14. Compact operators 83
15. Invariant subspaces 88
EXERCISES II 91
CHAPTER III, SPECTRAL THEORY OF COMPACT SELF ADJOINT OPERATORS 105
1. Example of an infinite dimensional generalization 106
2. The problem of existence of eigenvalues and eigenvectors 106
3. Eigenvalues and eigenvectors of operators of finite rank 108
4. Theorem of existence of eigenvalues 110
5. Spectral theorem 113
6. Basic systems of eigenvalues and eigenvectors 115
7. Second form of the spectral theorem 118
8. Formula for the inverse operator 119
9. Minimum-Maximum properties of eigenvalues 121
EXERCISES III 125
CHAPTER IV. SPECTRAL THEORY OF INTEGRAL OPERATORS 131
1. Hilbert-Schmidt theorem 131
2. Preliminaries for Mercer's theorem 134
3 . Mercer's theorem 136
4. Trace formula for integral operators 138
5. Integral operators as inverses of differential operators 139
6. Sturm-Liouville systems 142
EXERCISES IV 148
CHAPTER V. OSCILLATIONS OF AN ELASTIC STRING 153
1. The displacement function 153
2. Basic harmonic oscillations 155
3. Harmonic oscillations with an external force . 157
CHAPTER VI. OPERATIONAL CALCULUS WITH APPLICATIONS 159
1. Functions of a compact self adjoint operator 159
2. Differential equations in Hilbert space 165
3. Infinite systems of differential equations ... 167
4. Integro-differential equations 168
EXERCISES VI 170
CHAPTER VII. SOLVING LINEAR EQUATIONS BY ITERATIVE METHODS 73
1. The ma in theorem 173
2. Preliminaries for the proof 174
3. Proof of the main theorem 177
4. Application to integral equations 179
CHAPTER VIII. FURTHER DEVELOPMENTS OF THE SPECTRAL THEOREM 181
1. Simultaneous diagonalization 181
2. Compact normal operators 182
3. Unitary operators 184
4. Characterizations of compact operators 187
EXERCISES VIII 189
CHAPTER IX. BANACH SPACES 193
1. Definitions and examples 194
2. Finite dimensional normed linear spaces 196
3. Separable Banach spaces and Schauder bases 200
4. Conjugate spaces 201
5. Hahn-Banach theorem 203
EXERCISES IX 206
CHAPTER X. LINEAR OPERATORS ON A BANACH SPACE 211
1. Description of bounded operators 211
2. An approximation scheme 214
3. Closed linear operators 219
4. Closed graph theorem and its applications 221
5. Complemented subspaces and projections 224
6. The spectrum of an operator 226
7. Volterra Integral Operator 229
8. Analytic operator valued functions 231
EXERCISES X 232
CHAPTER XI. COMPACT OPERATORS ON A BANACH SPACES 237
1. Examples of compact operators 237
2. Decomposition of operators of finite rank 240
3. Approximation by operators of finite rank 241
H. Fredholm theory of compact operators 242
5. Conjugate operators on a Banach space 245
6. Spectrum of a compact operator 248
7. Applications 251
EXERCISES XI 253
CHAPTER XII. NON LINEAR OPERATORS 255
1. Fixed point theorem 255
2. Applications of the contraction mapping theorem 256
3. Generalizations 261
APPENDIX 1. COUNTABLE SETS AND SEPARABLE HILBERT SPACES 265
APPENDIX 2. LEBES6UE INTEGRATION AND Lp SPACES 267
APPENDIX 3. PROOF OF THE HAHN-BANACH THEOREM 273
APPENDIX 4. PROOF OF THE CLOSED GRAPH THEOREM 277
SUGGESTED READING 280
REFERENCES 281
INDEX 282
INTRODUCTION xi
CHAPTER I. HILBERT SPACES 1
1. Complex n-space 1
2. The Hilbert space I2 3
3. Definition of Hilbert space and its elementary properties 5
4. Distance from a point to a finite dimensional subspace 10
5. The Gram determinant 12
6. Incompatible systems of equations 16
7. Least squares fit 17
8. Distance to a convex set and projections onto subspaces 19
9. Orthonormal systems 21
10. Legendre polynomials 22
11. Orthonormal Bases 25
12. Fourier series 28
13. Completeness of the Legendre polynomials 30
14. Bases for the Hilbert space of functions on a square 31
15. Stability of orthonormal bases 33
16. Separable spaces 34
17. Equivalence of Hilbert spaces 36
18. Example of a non separable space 37
EXERCISES I 38
CHAPTER II. BOUNDED LINEAR OPERATORS ON HILBERT SPACES 51
1. Properties of bounded linear operators 51
2. Examples of bounded linear operators with estimates of norms 53
3. Continuity of a linear operator 57
4. Matrix representations of bounded linear operators 58
5. Bounded linear functionals 60
6. Operators of finite rank 63
7. Invertible operators 65
8. Inversion of operators by the iterative method 70
9. Infinite systems of linear equations 72
10. Integral equations of the second kind 74
11. Adjoint operators 77
12. Self adjoint operators 80
13. Orthogonal projections 82
14. Compact operators 83
15. Invariant subspaces 88
EXERCISES II 91
CHAPTER III, SPECTRAL THEORY OF COMPACT SELF ADJOINT OPERATORS 105
1. Example of an infinite dimensional generalization 106
2. The problem of existence of eigenvalues and eigenvectors 106
3. Eigenvalues and eigenvectors of operators of finite rank 108
4. Theorem of existence of eigenvalues 110
5. Spectral theorem 113
6. Basic systems of eigenvalues and eigenvectors 115
7. Second form of the spectral theorem 118
8. Formula for the inverse operator 119
9. Minimum-Maximum properties of eigenvalues 121
EXERCISES III 125
CHAPTER IV. SPECTRAL THEORY OF INTEGRAL OPERATORS 131
1. Hilbert-Schmidt theorem 131
2. Preliminaries for Mercer's theorem 134
3 . Mercer's theorem 136
4. Trace formula for integral operators 138
5. Integral operators as inverses of differential operators 139
6. Sturm-Liouville systems 142
EXERCISES IV 148
CHAPTER V. OSCILLATIONS OF AN ELASTIC STRING 153
1. The displacement function 153
2. Basic harmonic oscillations 155
3. Harmonic oscillations with an external force . 157
CHAPTER VI. OPERATIONAL CALCULUS WITH APPLICATIONS 159
1. Functions of a compact self adjoint operator 159
2. Differential equations in Hilbert space 165
3. Infinite systems of differential equations ... 167
4. Integro-differential equations 168
EXERCISES VI 170
CHAPTER VII. SOLVING LINEAR EQUATIONS BY ITERATIVE METHODS 73
1. The ma in theorem 173
2. Preliminaries for the proof 174
3. Proof of the main theorem 177
4. Application to integral equations 179
CHAPTER VIII. FURTHER DEVELOPMENTS OF THE SPECTRAL THEOREM 181
1. Simultaneous diagonalization 181
2. Compact normal operators 182
3. Unitary operators 184
4. Characterizations of compact operators 187
EXERCISES VIII 189
CHAPTER IX. BANACH SPACES 193
1. Definitions and examples 194
2. Finite dimensional normed linear spaces 196
3. Separable Banach spaces and Schauder bases 200
4. Conjugate spaces 201
5. Hahn-Banach theorem 203
EXERCISES IX 206
CHAPTER X. LINEAR OPERATORS ON A BANACH SPACE 211
1. Description of bounded operators 211
2. An approximation scheme 214
3. Closed linear operators 219
4. Closed graph theorem and its applications 221
5. Complemented subspaces and projections 224
6. The spectrum of an operator 226
7. Volterra Integral Operator 229
8. Analytic operator valued functions 231
EXERCISES X 232
CHAPTER XI. COMPACT OPERATORS ON A BANACH SPACES 237
1. Examples of compact operators 237
2. Decomposition of operators of finite rank 240
3. Approximation by operators of finite rank 241
H. Fredholm theory of compact operators 242
5. Conjugate operators on a Banach space 245
6. Spectrum of a compact operator 248
7. Applications 251
EXERCISES XI 253
CHAPTER XII. NON LINEAR OPERATORS 255
1. Fixed point theorem 255
2. Applications of the contraction mapping theorem 256
3. Generalizations 261
APPENDIX 1. COUNTABLE SETS AND SEPARABLE HILBERT SPACES 265
APPENDIX 2. LEBES6UE INTEGRATION AND Lp SPACES 267
APPENDIX 3. PROOF OF THE HAHN-BANACH THEOREM 273
APPENDIX 4. PROOF OF THE CLOSED GRAPH THEOREM 277
SUGGESTED READING 280
REFERENCES 281
INDEX 282
links
http://xinio.info/?http://ifile.it/8lwgr3v/86289.rar
RAR archive password: twilightzone
or
http://xinio.info/?http://ifile.it/8fgey2/t04782.rar
password: twilightzone
all of
type
djvu
(inlove)(inlove)(inlove)
type
djvu
(inlove)(inlove)(inlove)
