Let L0 be a given differential
operator with spectral matrix (ρij0). There is a concept of “closeness to (ρij0)” such
that for every positive matrix measure (ρij) which is “close to (ρij0)” there exists
some differential operator L for which (ρij) is a spectral matrix and there exists a
potentially computational technique by which L may be constructed from (ρij) and
(ρij0). The formulation of the “closeness to (ρij0)” concept and the presentation of
the techniques by which L may be constructed from (ρij) and (ρij0) are
referred to as the local inverse spectral problem, which is the subject of this
paper.
