Open AccessPositive resolving kernels and annihilators in linear inverse theory
Author(s) -
Huestis Stephen P.
Publication year - 1988
Publication title -
geophysical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0952-4592
DOI - 10.1111/j.1365-246x.1988.tb02276.x
Subject(s) - mathematics , annihilator , converse , inverse theory , equivalence (formal languages) , contradiction , simple (philosophy) , duality (order theory) , inverse , pure mathematics , calculus (dental) , mathematical analysis , algebra over a field , geometry , physics , deformation (meteorology) , meteorology , medicine , philosophy , dentistry , epistemology
SUMMARY 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.