Suppose that K is a linear space
of functions analytic in some domain D in the
complex plane. A sequence Λ = (λk) of distinct
points from D is said to be a set of
uniqueness for K if ƒ∈K and ƒ(λk) = 0 for all
k imply ƒ≡0. Depending on the
dispersion and the density of Λ on the one hand,
and the growth of the functions in
K on the other, one may often require only
|ƒ(λk)| [les ]ak for some sequence of positive
numbers ak, and still conclude that ƒ≡0
for ƒ∈K. Of particular interest are sharp
conditions on the decay of ak, which reflect
the interplay between growth and decay
of analytic functions.