Author | Sakhnovich, L. A. author |
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Title | Interpolation Theory and Its Applications [electronic resource] / by L. A. Sakhnovich |
Imprint | Dordrecht : Springer Netherlands, 1997 |
Connect to | http://dx.doi.org/10.1007/978-94-009-0059-2 |
Descript | XVIII, 197 p. online resource |
1.Operator Identities and Interpolation Problems -- 1.1. Operator identities and statement of the problem -- 1.2. A matrix inequality -- 1.3. A transformed inequality -- 1.4. The solution of non-degenerate interpolation problems -- 1.5. The Weyl discs -- 1.6. Degenerate problems, a regularization method -- 1.7. Examples -- 2. Interpolation Problems in the Unit Circle -- 2.1. Operator identities and statement of the problem -- 2.2. Abstract matrix inequality -- 2.3. A transformed inequality -- 2.4. The solution of non-degenerate interpolation problems -- 2.5. Examples -- 3. Hermitian-Positive Functions of Several Variables -- 3.1. Auxiliary section -- 3.2. Non-extendible Hermitian-positive functions of two variables (discrete case) -- 3.3. Non-extendible Hermitian-positive functions of three variables (discrete case) -- 3.4. Continuous variant of extension problem -- 3.5. Concrete examples instead of existence theorems -- 3.6. Non-negative polynomials which cannot be represented in the form of the squares sum -- 4. De Branges Spaces of Entire Functions -- 4.1. De Branges spaces -- 4.2. De Branges matrices -- 4.3. The Parseval Equality -- 4.4. A functional model -- 4.5. On the linear equivalence of operators -- 4.6. The Parseval equality (continuation) -- 5. Degenerate Problems (Matrix Case) -- 5.1. Canonical representations -- 5.2. Solution of matrix inequality -- 5.3. Degenerate problems in the unit circle -- 6. Concrete Interpolation Problems -- 6.1. Tangential problem -- 6.2. Interpolation problems for the class of bounded functions -- 6.3. Schur problem -- 6.4. The Nevanlinna-Pick problem in the circle -- 6.5. Generalized stationary processes -- 7. Extremal Problems -- 7.1. Extremal Interpolation Problem -- 7.2. Schur extremal problem -- 7.3. Nevanlinna-Pick extremal problem -- 7.4. Maximal jump problem -- 8. Spectral Problems for Canonical Systems of Difference Equations -- 8.1. Direct and Inverse Spectral Problems on the Half-axis -- 8.2. The connection of the canonical systems with the classical systems -- 8.3. Livsic-Brodskii nodes and spectral theory -- 8.4. Spectral problems on the axis -- 8.5. Weyl-Titchmarsh matrix functions -- 8.6. The inverse spectral problem on the axis -- 9. Integrable Nonlinear Equations (Discrete Case) -- 9.1. Evolution law of spectral data -- 9.2. Construction of hierarchy -- 10. On Semi-Infinite Toda Chain -- 10.1. Inverse problem and evolution of spectral data -- 10.2. Semi-infinite chain with a free end -- 10.3. The evolution law for the Toda chain with a fixed end -- 10.4. Analytical properties of the Weyl-Titchmarsh function -- 10.5. A half-finite chain with a fixed end, the solving procedure -- 10.6. Finite chain, solution procedure -- 11. Functions with an Operator Argument -- 11.1. Nevanlinna class functions with an operator argument -- 11.2. Positive functions with an operator argument -- 11.3. On Sarason scheme -- 11.4. Factorization formula -- Commentaries and Remarks