Characterization of Sets K for which H∞ K (D) is an Algebra - Part II

Let K ⊂ Z+ and define the set H∞K (D) to be the collection of all bounded analytic functions on the unit disk D in the complex plane whose kth derivative vanishes at zero for all k ∈ K. Depending on the choice of K, the set H∞K (D) may or may not be an algebra. We consider the case where K is infinite and show how to construct these sets.