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Time-variant Darlington synthesis and induced realizations

Pik D.

International Journal of Applied Mathematics and Computer Science

2001

Vol. 11, no 6

1331-1360

For a block lower triangular contraction T, necessary and sufficient conditions are given in order that there exist block lower triangular contractions T1,1, T2,1 and T2,2 such that Ut= [ T1,1 T ] T2,1 T2,2 is unitary. For the case when T1,1* and T2,2 have dense ranges, all such embeddings are described. Each unitary embedding of UT induces a contractive realization of T, and various properties of this realization are characterized in terms of the unitary embedding.