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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Extension and Interpolation of Linear Operators and Matrix Functions (Paperback, 1990 ed.)
Loot Price: R1,622
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Extension and Interpolation of Linear Operators and Matrix Functions (Paperback, 1990 ed.)
Series: Operator Theory: Advances and Applications, 47
Expected to ship within 10 - 15 working days
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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, ...
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