Interpolation spaces in the resolution of ill-posed problems

摘要

A number of applied problems connected with the interpretation of geophysical data leads to the resolution of ill-posed problems of the form A x = y(sub (delta)), where A is an integral operator and y(sub (delta)) - some measurements. In the resolution of these problems by the Tikhonov's variational method, the choice of the stabilizing functional is crucial and needs some a-priori informations about the exact solution. Here the norm of the interpolation spaces X(sub (theta),q,) which depends on two parameters 0 < (theta) < 1, 1 (<=) q < (infinity) is proposed as a stabilizing functional. The a-priori information about the exact solution is characterized by its membership in one of the interpolation spaces. (author). 9 refs. (Atomindex citation 27:046046)