INVERSE PROBLEM AND SINGULARITY OF THE INTEGRATION KERNEL

Many important problems in physics and other sciences can be formulate d in terms of the inverse problem of type n(y) = integral K(y/x)g(x) d x, where g(x) is unknown. We show that this problem can be completely solved for a quite general class of kernel K(y/x) by analytically dila ting n(y) and K(y/x) to the complex z plane, and by the analysis of th e singularity of the dilated kernel K(z/x). The formalism is also exte nded to multi-dimensional cases.