# Preparatory Lemmas

# 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.

*Keywords:*
convergence, mollifier, multi-index, moment vanishing condition, smooth function, integral

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.