Abstract. We give a new proof on the disk that a Pick problem can be solved by a rational function that is unimodular on the unit circle and for which the number of poles inside the disk is no more than the number of non-positive eigenvalues of the Pick matrix. We use this method to find rational solutions to Pick problems on the bidisk.
AMS Subject Classification
(1991): 30E05, 32E30
Keyword(s):
Nevanlinna--Pick interpolation,
Takagi problem,
rational interpolation,
degenerate Pick problem
Received April 13, 2012, and in revised form December 12, 2012. (Registered under 61/2012.)
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