A Topological Approach to Nevanlinna–Pick Interpolation
Tryphon T. Georgiou · SIAM Journal on Mathematical Analysis · 1987
We study the set of rational solutions of an $(N + 1)$-point Nevanlinna–Pick problem, that has degree bounded by N Based on the invariance of the topological degree of a certain mapping under deformation, we establish that when the $(N + 1)$-point Nevanlinna–Pick problem is solvable, then for any dissipation polynomial of degree N or less, there corresponds an interpolating function with dimension at most N Our results provide a novel topological proof for the sufficiency of Pick’s criterion for the solvability of the Nevanlinna–Pick problem, and also give a solution to an extended interpolation problem.