. C V ] 2 2 Ju l 2 00 5 , BOUNDARY NEVANLINNA – PICK INTERPOLATION PROBLEMS FOR GENERALIZED SCHUR FUNCTIONS
نویسنده
چکیده
is positive semidefinite for every choice of an integer n and of n points z1, . . . , zn ∈ D. The significance of this characterization for interpolation theory is that it gives the necessity part in the Nevanlinna-Pick interpolation theorem: given points z1, . . . , zn ∈ D and w1, . . . , wn ∈ C, there exists w ∈ S with w(zj) = wj for j = 1, . . . , n if and only if the associated Pick matrix P = [ 1−wiwj 1−zizj ] is positive semidefinite.
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