Weighted Bergman Spaces: Shift-Invariant Subspaces and Input/State/Output Linear Systems
It is well known that subspaces of the Hardy space over the unit disk which are invariant under the backward shift occur as the image of an observability operator associated with a discrete-time linear system with stable state-dynamics, as well as the functional-model space for a Hilbert space contr...
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| Published in: | Integral equations and operator theory Vol. 76; no. 3; pp. 301 - 356 |
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| Language: | English |
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01.07.2013
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| ISSN: | 0378-620X, 1420-8989 |
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| Abstract | It is well known that subspaces of the Hardy space over the unit disk which are invariant under the backward shift occur as the image of an observability operator associated with a discrete-time linear system with stable state-dynamics, as well as the functional-model space for a Hilbert space contraction operator, while forward shift-invariant subspaces have a representation in terms of an inner function. We discuss several variants of these statements in the context of weighted Bergman spaces on the unit disk. |
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| AbstractList | It is well known that subspaces of the Hardy space over the unit disk which are invariant under the backward shift occur as the image of an observability operator associated with a discrete-time linear system with stable state-dynamics, as well as the functional-model space for a Hilbert space contraction operator, while forward shift-invariant subspaces have a representation in terms of an inner function. We discuss several variants of these statements in the context of weighted Bergman spaces on the unit disk. |
| Author | Bolotnikov, Vladimir Ball, Joseph A. |
| Author_xml | – sequence: 1 givenname: Joseph A. surname: Ball fullname: Ball, Joseph A. organization: Department of Mathematics, Virginia Tech – sequence: 2 givenname: Vladimir surname: Bolotnikov fullname: Bolotnikov, Vladimir email: vladi@math.wm.edu organization: Department of Mathematics, The College of William and Mary |
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| Cites_doi | 10.1007/BF02395019 10.1016/0022-1236(85)90093-X 10.1007/978-1-4684-9330-6 10.1007/s00020-007-1502-4 10.1006/jfan.2000.3664 10.1016/j.jfa.2006.03.004 10.1006/jfan.2001.3874 10.2307/2159525 10.1016/j.jmaa.2006.10.076 10.1007/978-3-0348-8791-5 10.1007/BF02559553 10.1007/BF02392623 10.1007/s11045-006-0011-y 10.1090/S0894-0347-97-00244-0 10.1215/S0012-7094-77-04409-X 10.1090/S0002-9939-02-06721-7 10.1007/978-1-4612-0497-8 10.1007/s00020-012-1986-4 10.1007/BF02392585 10.1007/s11785-010-0101-6 10.1007/978-3-0348-8532-4 10.1515/crll.1961.208.102 10.1007/978-3-0348-8077-0_3 10.1090/surv/100 |
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| Keywords | Bergman space Operator-valued functions Beurling–Lax representations transfer-function realization 47A48 47A57 |
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| Title | Weighted Bergman Spaces: Shift-Invariant Subspaces and Input/State/Output Linear Systems |
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