Positive resolving kernels and annihilators in linear inverse theory
Stephen P. Huestis · Geophysical Journal International · 1988
In linear Backus-Gilbert theory, an equivalence is demonstrated between nonexistence of nonnegative resolving kernels, and the existence of strictly positive annihilators. If a positive annihilator exists, a simple proof by contradiction shows that all resolving kernels must have negative sidelobes. The converse follows by application of the duality theorem of linear programming.