Conclusions

The mathematical theory of stacking operators leads to the fundamental concept of asymptotic inversion. When the integral continuation operators are constructed by the asymptotic Green-function solution of the partial differential equation, they often appear to be asymptotically inverse to the reverse continuation.

The concept of the adjoint operator is fundamental for the practical least-square inversion. From a practical point of view, every linear operator, including the operators of stacking type, can be represented with a matrix, and the adjoint operator corresponds to the matrix transposition.

This paper fills the gap between the concept of asymptotically inverse operators and the concept of adjoint operators by introducing the notion of asymptotic pseudo-unitary stacking operators. To what extent this notion is useful for practical least-square inversion largely depends on the particular form of the inverted operator. Practical applications may require specialized numeric tests.