Time-variant Darlington Synthesis and Induced Realizations
نویسنده
چکیده
Let T be a block lower triangular contraction, i.e., a contractive operator T = (ti,j) ∞ i,j=−∞ acting from a doubly infinite Hilbert space direct sum ⊕∞ j=−∞Kj into a doubly infinite Hilbert space direct sum ⊕∞ j=−∞ Lj . The operator ti,j , which maps Kj into Li, is the (i, j)-th entry in the operator matrix representation of T relative to the natural Hilbert space direct sum decompositions. In this paper we study the problem of finding block lower triangular contractions T1,1, T2,1 and T2,2 such that the operator matrix
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