Theory and applications of intermediate operators. I: General results. (Q1195005)

Summary: Problems of the following kind are considered: \((Tu,v)_ H=(f,v)_ S\), \(f\in S\), \(u\in H\), \(\forall v\in H\), vector \(f\) is given, vector \(u\) is the ``unknown''. \(H\) is a subspace of the Hilbert space \(S\). \(T\) is a linear operator from \(H\) to \(H\) which satisfies suitable hypotheses. By using the theory of intermediate operators methods for the calculus of the ``Green operators'' and of the relevant ``Green functions'' are given. Explicit `` a priori'' estimates are obtained which are as close as we wish to the optimal ones.