The concept of concavity is generalized to discrete functions, u, satisfyin
g the nth order difference inequality, (-1)(n-k)Delta(n)u(m) greater than o
r equal to 0, m = 0, 1,..., N and the homogeneous boundary conditions, u(0)
= ... = u(k-1) = 0, u(N+k+1) = ... = u(N+n) = 0 for some k is an element o
f {1,..., n-1}. A piecewise polynomial is constructed which bounds u below.
The piecewise polynomial is employed to obtain a positive lower bound on u
(m) for m = k,..., N + k, where the lower bound is proportional to the supr
emum of u. An analogous bound is obtained for a related Green's function. (
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