A NEW RESULT ON THE SINGULAR VALUEASYMPTOTICS OF INTEGRATIONOPERATORS WITH WEIGHTS

摘要

It is an interesting question for the analysis oflinear ill-posed operator equations Ax = y and it seems to beof some importance for regularization theory whether a non-compact linear operator with non-closed range applied to acompact linear operator mapping between Hilbert spaces canalter the degree of ill-posedness determined by the singularvalue decay rate an (A) iu 0 as niu of the compact opera-tor A. For giving some more answer to that question we workin the space L~2(0,1) and focus on non-compact multiplication