Title | Matrix and Operator Valued Functions [electronic resource] : The Vladimir Petrovich Potapov Memorial Volume / edited by I. Gohberg, L. A. Sakhnovich |
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Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1994 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8532-4 |
Descript | XXVIII, 212 p. online resource |
The influence of V.P. Potapov and M.G. Krein on my scientific work -- 1. My first dissertation -- 2. A tilt toward operator theory -- 3. The results of Potapovโs group in network theory -- 4. Darlington method in the general theory of passive systems -- 5. Regular j-inner matrix functions and related generalized bitangential problems -- References -- The development of some of V.P. Potapovโs ideas. The geometric theory of operators in spaces with indefinite metric -- References -- On the Potapov theory of multiplicative representations -- References -- An operator approach to the Potapov scheme for the solution of interpolation problems -- I. Potapovโs method of solution of interpolation problems -- II. Operator identities and interpolation problems -- References -- Description of a class of functions which admit an approximation by rational functions with preassigned poles I -- 2. The class PCNM of pseudocontinuable functions -- 3. The Smirnov class N* -- 4. The weighted space PCH??(I+,I-) of pseudocontinuable meromorphic functions with prescribed denominators -- 5. G. Ts. Tumarkinโs theorem on functions which admit weighted approximation by a sequence of rational functions with preassigned poles -- 6. Formulation of the main approximation theorem -- 7. A fundamental approximation Lemma -- References -- An analysis and extension of V.P. Potapovโs approach to problems with applications to the generalized bi-tangential Schur-Nevanlinna-Pick problem and J-inner-outer factorization -- 1. Potapovโs approach to the Nevanlinna-Pick problem -- 2. An analysis of Potapovโs approach and the AIP -- 3. The abstract interpolation problem -- 4. The AIP and unitary extensions of an isometry -- 5. The generalized bi-tangential Schur-Nevanlinna-Pick (SNP) problem -- 6. Inner-outer factorization of J-contractive matrix-functions -- References -- On the theory of inverse problems for the canonical differential equation -- References -- Addendum -- Some properties of linear-fractional transformations and the harmonic mean of matrix functions -- References -- Modification of V.P. Potapovโs scheme in the indefinite case -- 0. Introduction -- 1. Preliminaries -- 2. Basic propositions -- 3. Extensions of the operator S -- 4. Examples -- References -- Inverse problems for equations systems -- 1. Introduction -- 2. Existence theorems -- 3. Classical examples -- 4. Uniqueness theorems -- References