  In the context of analytic functions on the open unit disk, a weighted
composition operator is simply a composition operator followed by a
multiplication operator. The class of weighted composition operators has an
important place in the theory of Banach spaces of analytic functions; for
instance, it includes all isometries on $H^p$ $(p\neq 2)$. Very recently it was
shown that only weighted composition operators preserve the class of outer
functions.
  The present paper considers a particular question motivated by applications:
Which smallest possible sets of test functions can be used to identify an
unknown weighted composition operator? This stems from a practical problem in
signal processing, where one seeks to identify an unknown minimum phase
preserving operator on $L^2(\real_+)$ using test signals.
  It is shown in the present paper that functions that determine weighted
composition operators are directly linked to the classical normal family of
schlicht functions. The main result is that a pair of functions $\{f,g\}$
distinguishes between any two weighted composition operators if and only if
there exists a zero-free function $h$ and a schlicht function $\sigma$ such
that $\spn\{f,g\}=\spn\{h\sigma,h\}$. This solves completely the underlying
signal processing problem and brings to light an intriguing geometric object,
the manifold of planes of the form $\spn\{h\sigma,h\}$. As an application of
the main result, it is proven that there exist compactly supported pairs in
$L^2(\real_+)$ that can be used to identify minimum phase preserving operators.
