Multiparameter Spectral Theory in Hilbert Space

Cover......Page 1
Tides in this series......Page 2
Title: Multiparameter Spectral Theory in Hilbert Space......Page 3
Copyright......Page 4
Dedication......Page 5
Preface......Page 7
Contents......Page 9
1 An introduction......Page 12
References......Page 18
2.1 The algebraic tensor product......Page 20
2.2 Hilbert tensor product of Hilbert spaces......Page 22
2.3 Tensor products of linear operators......Page 25
2.4 Functions of several commuting self-adjoint operators......Page 27
2.5 Solvability of a linear operator system......Page 29
References......Page 38
3.1 Introduction......Page 39
3.2 Multiparameter spectral theory......Page 41
3.3 Eigenvalues......Page 45
3.4 The case of compact operators......Page 48
References......Page 52
4.1 Introduction......Page 53
4.2 Commuting self-adjoint operators......Page 54
4.3 Multi-pabambtir spectral theory......Page 62
4.4 The compact case......Page 66
4. 5 An application to ordinary differential equations......Page 69
References......Page 71
5.1 Introduction......Page 73
5.2 An eigenvalue problem......Page 75
5.3 The factorisation of W......Page 77
5.4 An application to ordinary differential equations......Page 84
5.5 A comparison of the definiteness conditions......Page 88
References......Page 91
6.2 The problem......Page 92
6.3 Some applications to ordinary differential equations......Page 98
References......Page 101
7.1 Introduction......Page 102
7.2 Direct sums of Hilbert spaces......Page 103
7.3 Reduction of strongly coupled......Page 105
7.4 Spectbal theory for weakly coupled systems......Page 107
References......Page 109
8.1 Introduction......Page 110
8. 2 The fundamental reformulation......Page 112
8.3 Two-parameter spectral theory......Page 113
8.4 Concerning eigenvalues......Page 115
8.5 The case of unbounded operators......Page 117
8.6 An application to ordinary differential equations......Page 119
References......Page 120
9.1 Solvability of linear operator systems......Page 122
9.2 Multiparameter spectral theory for bounded operators......Page 123
9.3 Multiparameter spectral theory for unbounded operators......Page 124
9.5 Applications......Page 125
References......Page 126
Index......Page 127