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Schur-class multipliers on the Fock space: de Branges-Rovnyak reproducing kernel spaces and transfer-function realizations | | Joseph A. Ball
; Vladimir Bolotnikov
; Quanlei Fang
; PostScript
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; Other formats
; | | Date: |
20 Oct 2006 | | Subject: | Classical Analysis and ODEs | | Abstract: | We introduce and study a Fock-space noncommutative analogue of reproducing kernel Hilbert spaces of de Branges-Rovnyak type. Results include: use of the de Branges-Rovnyak space ${mathcal H}(K_{S})$ as the state space for the unique (up to unitary equivalence) observable, coisometric transfer-function realization of the Schur-class multiplier $S$, realization-theoretic characterization of inner Schur-class multipliers, and a calculus for obtaining a realization for an inner multiplier with prescribed left zero-structure. In contrast with the parallel theory for the Arveson space on the unit ball ${mathbb B}^{d} subset {mathbb C}^{d}$ (which can be viewed as the symmetrized version of the Fock space used here), the results here are much more in line with the classical univariate case, with the extra ingredient of the existence of all results having both a ``left’’ and a ``right’’ version. | | Source: | arXiv, math/0610635 | | Services: | Forum | Review | PDF | Favorites | |
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