{"product_id":"schur-functions-operator-colligations-and-daniel-alpay-9783764357634","title":"Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces","description":"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\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Daniel Alpay, Aad Dijksma, James Rovnyak\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3764357630\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783764357634\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Birkhauser\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 07\/15\/1997\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 252\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.33lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.61h x 6.69w x 0.63d","brand":"Daniel Alpay","offers":[{"title":"Hardcover","offer_id":44311403299071,"sku":"9783764357634","price":99.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_b2224285-ef1b-4b7f-81fd-323b78758787.jpg?v=1695722615","url":"https:\/\/www.whiterainbookhouse.com\/products\/schur-functions-operator-colligations-and-daniel-alpay-9783764357634","provider":"WR Book House","version":"1.0","type":"link"}