{"product_id":"extension-and-interpolation-of-linear-operators-and-matrix-functions-9783764325305","title":"Extension and Interpolation of Linear Operators and Matrix Functions","description":"\u003cp\u003e • Author(s): I. Gohberg\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Birkhauser\u003cbr\u003e • BISAC: General\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe 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, . . .\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Hardcover","offer_id":45282417541271,"sku":"9783764325305","price":3633.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783764325305.webp?v=1769302087","url":"https:\/\/atlanticbooks.com\/products\/extension-and-interpolation-of-linear-operators-and-matrix-functions-9783764325305","provider":"Atlantic Books","version":"1.0","type":"link"}