Extension and Interpolation of Linear Operators and Matrix Functions (Operator Theory: Advances And Applications)

I. Gohberg

ISBN 10: 3764325305 / ISBN 13: 9783764325305

Editore: Birkh�user Basel 1990-10-01, 1990

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Codice articolo 6666-IUK-9783764325305

Dati bibliografici

• Titolo: Extension and Interpolation of Linear Operators and Matrix Functions (Operator Theory: Advances And Applications)
• Editore: Birkh�user Basel 1990-10-01
• Data di pubblicazione: 1990
• Lingua: Inglese
• ISBN 10: 3764325305
• ISBN 13: 9783764325305
• Rilegatura: Paperback
• Condizione: New

Descrizione articolo

Riassunto

The classicallossless inverse scattering (LIS) problem of network theory is to find all possible representations of a given Schur function s(z) (i. e. , a function which is analytic and contractive in the open unit disc D) in terms of an appropriately restricted class of linear fractional transformations. These linear fractional transformations corre­ spond to lossless, causal, time-invariant two port networks and from this point of view, s(z) may be interpreted as the input transfer function of such a network with a suitable load. More precisely, the sought for representation is of the form s(Z) = -{ -A(Z)SL(Z) + B(z)}{ -C(Z)SL(Z) + D(z)} -1 , (1. 1) where "the load" SL(Z) is again a Schur function and _ [A(Z) B(Z)] 0( ) (1. 2) Z - C(z) D(z) is a 2 x 2 J inner function with respect to the signature matrix This means that 0 is meromorphic in D and 0(z)* J0(z) ::5 J (1. 3) for every point zED at which 0 is analytic with equality at almost every point on the boundary Izi = 1. A more general formulation starts with an admissible matrix valued function X(z) = [a(z) b(z)] which is one with entries a(z) and b(z) which are analytic and bounded in D and in addition are subject to the constraint that, for every n, the n x n matrix with ij entry equal to X(Zi)J X(Zj )* i,j=l, . . .

Contenuti

Realization and factorization for rational matrix functions with symmetries.- Lossless inverse scattering and reproducing kernels for upper triangular operators.- Zero-pole structure of nonregular rational matrix functions.- Structured interpolation theory.- Extension theorems for contraction operators on Krein spaces.