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A sequence (a_n)_{n\in\mathbb{N}} is said to converge to a limit l if given \varepsilon > 0, there exists some N_\varepsilon \in \mathbb{N} such that

\vert a_n - l \vert < \varepsilon

for all n>N_\varepsilon.

Given 1\le p < \infty, the Hardy space H^p(\mathbb{D}) is the collection of analytic functions f for which the norm

\|f\|^p = \sup_{r<1}\int_\mathbb{T} |f(rt)|^{1/p} dm(t)

is finite. Here m denotes normalised Lebesgue measure on the unit circle \mathbb{T}.

Hi guys,

Thanks to the (so-far) two of you who’ve inexplicably decided to sign up to the twitter account @sammaths. This is just a test to see if I’ve managed to get my teaching blog to automatically send out updates on Twitter.

Sorry to have bothered you!
SJE

Hi there,

I note that for now at least, no-one is likely to be looking out for this blog. It was created in June 2010, at a time when I had no specific teaching to do, so I guess that was inevitable, but all the same, it would be good to get some practice, so if any undergraduate mathematicians happen to stumble here, feel free to ask me to write a post on some topic of pure mathematics that you don’t understand and I’ll give it a go. Hopefully in the new term I’ll have a bit more to say, though for the moment at least, my job is mostly research, so I’m teaching for fun!

Best wishes,

SJE

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