Operator Methods in Mathematical Physics: Conference on Operator Theory, Analysis and Mathematical Physics (OTAMP) 2010, Bedlewo, Poland

Cover......Page 1
Conference on Operator Theory, Analysis and Mathematical Physics (OTAMP) 2010,\rBedlewo, Poland......Page 4
Contents......Page 8
Introduction......Page 10
Inverse Scattering for Non-classical Impedance Schrödinger Operators......Page 12
1. Introduction......Page 13
1.1. Basic definitions......Page 15
1.2. Miura potentials: the case of absolutely continuous p......Page 16
1.3. A physical example with discontinuous impedance......Page 18
1.4. Some singular impedance Schr¨odinger operators not discussed......Page 20
2.1. The continuous case......Page 21
2.2. The discrete case......Page 25
3.1. Jost solutions......Page 26
3.2. The scattering data......Page 31
3.3. Reconstruction of the transmission coefficient......Page 32
3.4. The inverse problem......Page 34
3.5. Sobolev properties of the scattering mappings......Page 37
4. The case of discontinuous impedance function......Page 38
4.2. Jost solutions and the scattering data......Page 39
4.3. Transformation operators......Page 42
4.4. Derivation of the Marchenko equation......Page 43
4.6. Solution of the Zakharov–Shabat system......Page 44
4.7. The inverse scattering problem......Page 46
4.8. Some generalizations......Page 47
Acknowledgement......Page 48
References......Page 49
1. Introduction......Page 54
2. Perturbations of the free Jacobi matrix......Page 57
3. Finite gap Jacobi matrices......Page 59
4. Infinite gap Jacobi matrices......Page 63
References......Page 65
1.1. Introduction......Page 67
1.2. The BCS functional......Page 68
1.2.1. The translation-invariant case......Page 69
1.4. Main results......Page 71
1.5. The coefficients in the GL functional......Page 72
2. Sketch of the proof......Page 73
3. Semiclassics......Page 75
4. Upper bound......Page 76
5.1. The relative entropy......Page 78
5.2. A priori estimates on α......Page 79
5.3. Decomposition of α......Page 81
5.4. The lower bound......Page 84
6.1. Preliminaries......Page 88
6.2. Proof of Theorem 3.1......Page 89
6.3. Proof of Theorem 3.2......Page 95
References......Page 97
1. Introduction......Page 99
2. Mathematical background......Page 101
3. Diagonalising the spectral density matrix......Page 105
4. The case of simple spectrum......Page 109
References......Page 114
1. Introduction......Page 116
2. Neumann problem for a strip on the cylinder......Page 119
3. Extension to minimal k-partitions of C(b)......Page 122
4. Generalization to other thin domains......Page 123
References......Page 124
Jacobi and CMV Matrices with Coefficients of Generalized Bounded Variation......Page 125
Acknowledgement......Page 128
References......Page 129
1. Introduction......Page 130
2. Main results......Page 133
3. Dominated Ergodic Theorem......Page 135
4. Converse Dominated Ergodic Theorem......Page 139
5. Pointwise Ergodic Theorem......Page 141
Orlicz spaces......Page 142
Lorentz spaces......Page 144
Orlicz-Lorentz spaces......Page 145
Order convergence of conditional expectations......Page 146
Convergence in norm......Page 147
References......Page 148
1. Introduction......Page 150
2. The main lemma......Page 151
3. Application to infinite systems......Page 153
4. Extension to general von Neumann algebras......Page 154
Acknowledgment......Page 155
References......Page 156
1. Introduction......Page 157
2. On symmetric operators with not necessarily dense domain......Page 158
3. A review on de Branges spaces with zero-free functions......Page 163
4. A functional model for operators in S(H)......Page 165
5. Spectral characterization......Page 167
6. Concluding remarks......Page 168
References......Page 169
1. Introduction and main results......Page 171
2. Selection of the main component in the asymptotics......Page 172
3. Estimation of the remainder......Page 178
References......Page 182