Math 6420 • PDE

\begin{enumerate}
\item[(a)] Define what is meant by a precompact (or sequentially compact) set and what is
meant by a compact linear operator, assuming linear operators and bounded sets have been
already been defined.

\item[(b)] If \(K\) is a compact linear operator and if \(\{\phi_n\}\) is an infinite set of
orthonormal functions then (using Bessel's inequality, if needed) show that
\[
  \lim_{n\to\infty}K\phi_n=0.
\]
\end{enumerate}