On minimal splitting subspaces and markovian representations |
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| Authors: | Anders Lindquist Giorgio Picci Guy Ruckebusch |
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| Affiliation: | (1) Department of Mathematics, University of Kentucky, 40506 Lexington, Kentucky, USA;(2) Laboratorio per Ricerche di Dinamica dei Sistemi e di Elettronica Biomedica, Consiglio Nazionale delle Ricerche, 35100 Padova, Italy;(3) Centre de Mathematiques Appliquées, Ecole Polytechnique, 91128 Palaiseau Cedex, France |
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| Abstract: | Given a Hilbert spaceH, letH
1 andH
2 be two arbitrary subspaces. The problem of finding all minimal splitting subspaces ofH with respect toH
1 andH
2 is solved. This result is applied to the stochastic realization problem. Each minimal stochastic realization of a given vector processy defines a family of state spaces. It is shown that these families are precisely those families of minimal splitting subspaces (with respect to the past and the future ofy) which satisfy a certain growth condition.Research sponsored by the Air Force Office of Scientific Research under Grant No. AFOSR-78-3519. |
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