Direct and inverse results in variable Hilbert scales
Let us consider a non-negative self-adjoint compact and injective operator \(H\) acting in a Hilbert space \(X\). With the help of a singular decomposition of \(H\) and of some set \(\{ \psi \}\) of continuous and strictly convex functions acting from \([0,a]\) in \([0,\infty )\) a scale of Hilbert spaces \(H_\psi ^H\) is introduced. These spaces are studied in the context of approximation theory. Namely, in terms of so-called general sourse conditions, direct and inverse theorems for approximation by a sequence of finite dimensional subspaces of \(X\) are established.
scientific article; zbMATH DE number 5501948
scientific article