Extension and interpolation of linear operators and matrix functions. Operator theory; Bd. 47.

Gohberg, I.

ISBN 10: 3764325305 / ISBN 13: 9783764325305

Published by Basel, Birkhäuser, 1990

About this Item

Ex-library with stamp and library-signature. GOOD condition, some traces of use. C-03689 3764325305 Sprache: Englisch Gewicht in Gramm: 1050.

Seller Inventory # 2489612

Bibliographic Details

• Title: Extension and interpolation of linear operators and matrix functions. Operator theory; Bd. 47.
• Publisher: Basel, Birkhäuser
• Publication Date: 1990
• Language: English
• ISBN 10: 3764325305
• ISBN 13: 9783764325305
• Binding: Hardcover
• Seller catalogs:
  • SA MATHEMATIK

About this title

Synopsis

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, . . .