Abstract

The Grassmannian/Kreĭn-space approach to interpolation theory introduced in the 1980s gives a Kreĭn-space geometry approach to arriving at the resolvent matrix which parametrizes the set of solutions to a Nevanlinna- Pick interpolation or Nehari-Takagi best-approximation problem. We review the basics of this approach and then discuss recent extensions to multivariable settings which were not anticipated in the 1980s.KeywordsKreĭn spacemaximal negative and maximal positive subspacesgraph spacesprojective spaceBeurling-Lax representations

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