  Operationally, index functions of variable Hilbert scales can be viewed as
generators for families of spaces and norms. Using a one parameter family of
index functions based on the dilations of a given index function, a new class
of scales (dilational Hilbert scales (DHS)) is derived which generates new
interpolatory inequalities (dilational interpolatory inequalities (DII)) which
have the ordinary Hilbert scales (OHS) interpolatory inequalities as special
cases. They therefore represent a one-parameter family generalization of OHS,
and are a precise and concise subset of VHS approriate for deriving error
estimates for deconvolution. The role of the Hilbert scales in deriving error
estimates for the approximate solution of inverse problems is discussed along
with an application of DHS to deconvolution sharpening.
