  We prove a weak version of Hardy's uncertainty principle using properties of
the prolate spheroidal wave functions (PSWFs). We describe the eigenvalues of
the sum of a time limiting operator and a band limiting operator acting on
L2(R). A weak version of Hardy's uncertainty principle follows from the
asymptotic behavior of the largest eigenvalue as the time limit and the band
limit approach infinity. An asymptotic formula for this eigenvalue is obtained
from its well-known counterpart for the prolate integral operator.
