Abstract :

A Hilbert scale is a family of Hilbert spaces Hs,s∈RHs,s∈R such that for every s,t∈Rs,t∈R with s < t, Ht⊆HsHt⊆Hs and the inclusion operator is continuous. Given a Hibert space, we show how to construct a Hilbert scale with H0=HH0=H using the concept of Gelfand triple and give examples of Hilbert scales which are generated by compact operators between Hilbert spaces as well as closed densely defined unbounded operators. Citing results from some of the recent work of the author, we discuss the use of Hilbert scales while deriving error estimates for ill-posed operator equations.