Author | Sakhnovich, Lev A. author |
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Title | Spectral Theory of Canonical Differential Systems. Method of Operator Identities [electronic resource] / by Lev A. Sakhnovich |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1999 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8713-7 |
Descript | VI, 202 p. online resource |
1 Factorization of Operator-valued Transfer Functions -- 1.1 Realization of operator-valued functions -- 1.2 A factorization method -- 1.3 Factorization of rational operator-valued functions -- 2 Operator Identities and S-Nodes -- 2.1 Elementary properties of S-nodes -- 2.2 Symmetric S-nodes -- 2.3 Inherited properties of factors -- 3 Continual Factorization -- 3.1 The main continual factorization theorem -- 3.2 Bounded operator-valued functions -- 4 Spectral Problems on the Half-line -- 4.1 Basic notions of spectral theory -- 4.2 Direct and inverse spectral problems -- 4.3 Livลกic-Brodski? nodes and the spectral theory of canonical systems -- 5 Spectral Problems on the Line -- 5.1 Spectral data of a canonical system -- 5.2 Spectral problems and S-nodes -- 5.3 The inverse spectral problem -- 6 Weyl-Titchmarsh Functions of Periodic Canonical Systems -- 6.1 Multipliers and their behavior -- 6.2 Weyl-Titchmarsh functions -- 6.3 Singular points of the Weyl-Titchmarsh matrix function -- 7 Division of Canonical Systems into Subclasses -- 7.1 An effective solution of the inverse problem -- 7.2 Two principles of dividing a class of canonical systems into subclasses -- 8 Uniqueness Theorems -- 8.1 Monodromy matrix and uniqueness theorems -- 8.2 Spectral data and uniqueness theorems -- 9 Weyl Discs and Points -- 9.1 Basic notions -- 9.2 Symmetric operators and deficiency indices -- 9.3 Weyl-Titchmarsh matrix functions on the line -- 9.4 Weyl-Titchmarsh matrix function of a system with shifted argument -- 10 A Class of Canonical Systems -- 10.1 Asymptotic formulas -- 10.2 Spectral analysis -- 10.3 Transformed canonical systems -- 10.4 Dirac-type systems -- 10.5 An inverse problem -- 10.6 On the limit Titchmarsh-Weyl function -- 11 Classical Spectral Problems -- 11.1 Generalized string equation (direct spectral problem) -- 11.2 Matrix Sturm-Liouville equation (direct spectral problem) -- 11.3 Inverse spectral problem -- 12 Nonlinear Integrable Equations and the Method of the Inverse Spectral Problem -- 12.1 Evolution of the spectral data -- 12.2 Some classical nonlinear equations -- 12.3 On the unique solvability of the mixed problem -- 12.4 A hierarchy of nonlinear equations and asymptotic behavior of Weyl-Titchmarsh functions -- Comments -- References