Boundary Nevanlinna-Pick interpolation via reduction and augmentation
نویسندگان
چکیده
We give an elementary proof of Sarason’s solvability criterion for the Nevanlinna-Pick problem with boundary interpolation nodes and boundary target values. We also give a concrete parametrization of all solutions of such a problem. The proofs are based on a reduction method due to Nevanlinna and the fact that reduction of functions corresponds to Schur complementation of the corresponding Pick matrices.
منابع مشابه
. C V ] 2 2 Ju l 2 00 5 , BOUNDARY NEVANLINNA – PICK INTERPOLATION PROBLEMS FOR GENERALIZED SCHUR FUNCTIONS
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 ...
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