Extension And Interpolation Of Linear Operators And Matrix Functions

Description: Please refer to the section BELOW (and NOT ABOVE) this line for the product details - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Title:Extension And Interpolation Of Linear Operators And Matrix FunctionsISBN13:9783764325305ISBN10:3764325305Author:Gohberg, I. (Author)Description: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, Binding:Hardcover, HardcoverPublisher:SPRINGER NATUREPublication Date:1990-10-01Weight:0.93 lbsDimensions:0.66'' H x 9'' L x 6'' WNumber of Pages:305Language:English

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