Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces

Von Alpay, Daniel /Dijksma, Aad /Rovnyak, James /Snoo, Hendrik de

ISBN 10: 3764357630 / ISBN 13: 9783764357634

Edité par Springer Basel, 1997

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Zustand: Sehr gut | Seiten: 3 | Sprache: Englisch | Produktart: Bücher.

N° de réf. du vendeur 776364/2

Détails bibliographiques

• Titre: Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces
• Éditeur: Springer Basel
• Date de parution: 1997
• Langue: anglais
• ISBN à 10 chiffres: 3764357630
• ISBN à 13 chiffres: 9783764357634
• Reliure: Couverture rigide
• État de l'article: Sehr gut
• Catalogues du vendeur:
  • Bücher

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Synopsis

1: Pontryagin Spaces and Operator Colligations.- 1.1 Reproducing kernel Pontryagin spaces.- 1.2 Operator colligations.- 1.3 Julia operators and contractions.- 1.4 Extension of densely defined linear relations.- 1.5 Complementation and reproducing kernels.- A. Complementation in the sense of de Branges.- B. Applications to reproducing kernel Pontryagin spaces.- 2: Schur Functions and their Canonical Realizations.- 2.1 Pontryagin spaces ?(S), ?($$ \widetilde{S} $$ ), and D(S).- 2.2 Canonical coisometric and isometric realizations.- 2.3 Canonical unitary realization.- 2.4 Unitary dilations of coisometric and isometric colligations.- 2.5 Classes SK(F, B).- A. Definition and basic properties.- B. Conformally invariant view.- C. Application to factorization of operator-valued functions.- D. A non-holomorphic kernel.- 3: The State Spaces.- 3.1 Invariance under difference quotients.- 3.2 Spaces ?(S).- 3.3 Spaces ?$$ \widetilde{S} $$.- 3.4 Spaces D(S).- 3.5 Examples and miscellaneous results.- A. Rational unitary functions.- B. Symmetry in the state spaces.- C. Some consequences of Leech's theorem.- D. The scalar case: S(z)? ?(S) if and only if $$ \widetilde{S} $$(z) ? ?($$ \widetilde{S} $$).- 4: Structural Properties.- 4.1 Factorization and invariant subspaces.- A. Inclusion of spaces ?(S).- B. Inclusion of spaces D (S).- 4.2 Kre?n-Langer factorization.- A. Existence and properties.- B. Strongly regular representations.- 4.3 The Potapov-Ginzburg transform.- 4.4 Applications to the realization theory.- A. Kre?n space inner and outer spaces F andB.- B. Other base points.- C. Examples.- 4.5 Canonical models.- Epilogue: Open Questions and Directions for Further Work.- Appendix: Some Finite-Dimensional Spaces.- Notes.- References.- Notation Index.- Author Index.