Preparatory Lemmas

This chapter prepares for the proof by introducing a method concerning the general rate of convergence of mollifiers. The lemma takes into account the multi-index, the moment vanishing conditions, and smooth functions. An explanation for reducing the number of minus signs appearing in the proof is offered. The case N = 2 of the above lemma suffices for the proof of the main theorem. The chapter considers another way to work out the details relating to the lemma, which will be repeatedly used in the remainder of the proof. In particular, it describes functions whose integrals are not normalized to 1, but which satisfy the same type of estimates as ∈subscript Element.