{"product_id":"schur-functions-operator-colligations-and-reproducing-kernel-pontryagin-spaces-hardcover","title":"Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces - Hardcover","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eDaniel Alpay\u003c\/b\u003e (Author), \u003cb\u003eAad Dijksma\u003c\/b\u003e (Author), \u003cb\u003eJames Rovnyak\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e1: 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.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 252\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.63 x 9.61 x 6.69 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e March 27, 1998\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":47337413148921,"sku":"9783764357634","price":160.38,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0789\/2782\/3097\/files\/efCBzO-a0s9783764357634.webp?v=1769679313","url":"https:\/\/bookscloud.io\/products\/schur-functions-operator-colligations-and-reproducing-kernel-pontryagin-spaces-hardcover","provider":"BooksCloud Book Dropshipping","version":"1.0","type":"link"}