عنوان

Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces

شابک

9783034889087

شابک

9783034898232

شماره

b406301

عنوان اصلي

Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces

نام عام مواد

[Book]

نام نخستين پديدآور

by Daniel Alpay, Aad Dijksma, James Rovnyak, Hendrik Snoo.

محل نشرو پخش و غیره

Basel :

نام ناشر، پخش کننده و غيره

Imprint: Birkhäuser,

تاریخ نشرو بخش و غیره

1997.

عنوان فروست

Operator Theory Advances and Applications ;

مشخصه جلد

96

متن يادداشت

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.

بدون عنوان

0

متن يادداشت

Generalized Schur functions are scalar- or operator-valued holomorphic functions such that certain associated kernels have a finite number of negative squares. This book develops the realization theory of such functions as characteristic functions of coisometric, isometric, and unitary colligations whose state spaces are reproducing kernel Pontryagin spaces. This provides a modern system theory setting for the relationship between invariant subspaces and factorization, operator models, Krein-Langer factorizations, and other topics. The book is intended for students and researchers in mathematics and engineering. An introductory chapter supplies background material, including reproducing kernel Pontryagin spaces, complementary spaces in the sense of de Branges, and a key result on defining operators as closures of linear relations. The presentation is self-contained and streamlined so that the indefinite case is handled completely parallel to the definite case.

شماره استاندارد بين المللي کتاب و موسيقي

9783034898232

عنوان

Springer eBooks

موضوع مستند نشده

Engineering.

موضوع مستند نشده

Mathematics.

مستند نام اشخاص تاييد نشده

Alpay, Daniel.

مستند نام اشخاص تاييد نشده

Dijksma, Aad.

مستند نام اشخاص تاييد نشده

Rovnyak, James.

مستند نام اشخاص تاييد نشده

Snoo, Hendrik.

مستند نام تنالگان تاييد نشده

SpringerLink (Online service)

تاريخ عمليات

20190303135636.0

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y