Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Can someone point me to a proof of the Hardy-Littlewood Tauberian theorem, that is suitable enough to be shown to high school students? (with knowledge of calculus, sequences and series of course)

share|cite|improve this question
Why should high-school students bother about Tauberian theorems? Ask 100 professional mathematicians what Tauberian theorems are all about, and you will get $\leq1$ usable response. – Christian Blatter Sep 4 '12 at 14:45
up vote 4 down vote accepted

Have you looked at the presentation in Titchmarsh's Theory of Functions (Section 7.5)? The only non-elementary part of the argument is Weierstrass's approximation theorem, which you can probably assume as a fact. The preliminary material given also include an "easy" special case where the exposition certainly can be understood by someone with knowledge of calculus, sequences, and series.

share|cite|improve this answer
Unfortunately, I've been unable to get a hold of a copy of Titchmarsh's book so far. – Ishihara Sep 4 '12 at 11:55
It is available on the Internet Archive. – Willie Wong Sep 4 '12 at 12:05
Found it, thank you. – Ishihara Oct 1 '12 at 15:27

Take a look at Chapter 1, sections 11 and 12 of Tauberian Theory: A Century of Development by Jacob Korevaar. He also has many references.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.