The number of functions defining interpolating varieties

Abstract

In this paper, we prove that if a disjoint union of a countable number of complex affine subspaces is interpolating for the Hörmander algebra, then it can be written as the common zero set of α+1 functions in the Hörmander algebra, where α is the maximum number of codimensions of the complex affine subspaces. Finally, we prove with an example in one complex variable that the number α+1 is lowest.