Constructive Function Theory

Abstract

The goal of this section is the construction, by means of sums and products of simpler functions, of holomorphic functions with prescribed behavior. In what follows, when we speak of a sequence of complex numbers we ordinarily mean a sequence with multiplicity, so that a function taking some value at a point of the sequence must take that value with the appropriate multiplicity. We also exclude the trivial function f ≡ 0 unless otherwise noted.