Author | Alpay, Daniel. author |
---|---|
Title | Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces [electronic resource] / by Daniel Alpay, Aad Dijksma, James Rovnyak, Hendrik de Snoo |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1997 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8908-7 |
Descript | XI, 232 p. online resource |
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 -- 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) -- 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 -- 4: Structural Properties -- 4.1 Factorization and invariant subspaces -- 4.2 Kre?n-Langer factorization -- 4.3 The Potapov-Ginzburg transform -- 4.4 Applications to the realization theory -- 4.5 Canonical models -- Epilogue: Open Questions and Directions for Further Work -- Appendix: Some Finite-Dimensional Spaces -- Notes -- References -- Notation Index -- Author Index