Spectral theory of canonical systems / Christian Remling.

Por: Remling, Christian [author.]Series De Gruyter studies in mathematics ; 70Editor: Berlin ; Boston : De Gruyter, c2018Descripción: x, 194 pages ; 25 cmTipo de contenido: text Tipo de medio: unmediated Tipo de portador: volumeISBN: 9783110562026 (print : alk. paper)Tema(s): Spectral theory (Mathematics)Otra clasificación: 34-02 (30E05 30H15 34B20 34L05 46E22 47A06)
Contenidos:
 Contents
 Preface—VII
asic definitions — [1]
Canonical systems — [1]
Singular intervals — [5]
Transformations — [6]
The Hilbert space L2H — [9]
Notes [10]
Symmetric and self-adjoint relations —11
The minimal and maximal relations of a canonical system —11
Von Neumann theory of symmetric relations —19
Self-adjoint realizations of canonical systems — [24]
The multi-valued part — [28]
More on deficiency indices — [32]
Notes [34]
Spectral representation — [35]
Spectral representation of relations — [35]
The resolvent as an integral operator — [36]
A limit point/limit circle criterion [39]
Weyl theory [40]
Spectral representation of canonical systems — [49]
General boundary conditions — [56]
Two limit point endpoints — [58]
Notes [67]
Transfer matrices and de Branges spaces — [69]
Review of complex analysis — [69]
De Branges spaces — [72]
Spectral representation and de Branges spaces — [76]
Transfer matrices — [84]
Regular de Branges spaces — [93]
The type of a transfer matrix — [95]
Transfer matrices and singular Intervals — [97]
Notes [103]
5 Inverse spectral theory —105
5.1 Introduction —105
5.2 Metrics on canonical systems and spectral data —106
5.3 Existence of a canonical system with given m function —112
5.4 The ordering theorem for de Branges spaces —116
5.5 Existence of a canonical system with given transfer matrix [128]
5.6 Uniqueness —131
5.7 Notes —135
6 Some applications —139
6.1 Generalized and classical moment problems and the Nevanlinna parametrization —139
6.2 Existence of moments —145
6.3 Diagonal canonical systems —148
6.4 Dirac systems —151
6.5 Notes —157
7 The absolutely continuous spectrum —159
7.1 Twisted shifts and Toda maps —159
7.2 Convergence of Herglotz functions —163
7.3 Reflectionless canonical systems —171
7.4 Semi-continuity of R and ∑ac —174
7.5 Reflectionless limit points —178
7.6 Notes [187]
 Bibliography—189
 Index—193
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Incluye referencias bibliográficas (páginas 189-191) e índice.

Contents --
Preface—VII --
asic definitions — [1] --
Canonical systems — [1] --
Singular intervals — [5] --
Transformations — [6] --
The Hilbert space L2H — [9] --
Notes [10] --
Symmetric and self-adjoint relations —11 --
The minimal and maximal relations of a canonical system —11 --
Von Neumann theory of symmetric relations —19 --
Self-adjoint realizations of canonical systems — [24] --
The multi-valued part — [28] --
More on deficiency indices — [32] --
Notes [34] --
Spectral representation — [35] --
Spectral representation of relations — [35] --
The resolvent as an integral operator — [36] --
A limit point/limit circle criterion [39] --
Weyl theory [40] --
Spectral representation of canonical systems — [49] --
General boundary conditions — [56] --
Two limit point endpoints — [58] --
Notes [67] --
Transfer matrices and de Branges spaces — [69] --
Review of complex analysis — [69] --
De Branges spaces — [72] --
Spectral representation and de Branges spaces — [76] --
Transfer matrices — [84] --
Regular de Branges spaces — [93] --
The type of a transfer matrix — [95] --
Transfer matrices and singular Intervals — [97] --
Notes [103] --
5 Inverse spectral theory —105 --
5.1 Introduction —105 --
5.2 Metrics on canonical systems and spectral data —106 --
5.3 Existence of a canonical system with given m function —112 --
5.4 The ordering theorem for de Branges spaces —116 --
5.5 Existence of a canonical system with given transfer matrix [128] --
5.6 Uniqueness —131 --
5.7 Notes —135 --
6 Some applications —139 --
6.1 Generalized and classical moment problems and the Nevanlinna parametrization —139 --
6.2 Existence of moments —145 --
6.3 Diagonal canonical systems —148 --
6.4 Dirac systems —151 --
6.5 Notes —157 --
7 The absolutely continuous spectrum —159 --
7.1 Twisted shifts and Toda maps —159 --
7.2 Convergence of Herglotz functions —163 --
7.3 Reflectionless canonical systems —171 --
7.4 Semi-continuity of R and ∑ac —174 --
7.5 Reflectionless limit points —178 --
7.6 Notes [187] --
Bibliography—189 --
Index—193 --

MR, MR3890099

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