The Takagi problem on the disk and bidisk
  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. 
Jim Agler, Joseph A. Ball, John E. McCarthy
math.FA math.CV