CONTINUOUS FRAMES IN HILBERT-SPACE

The standard theory of frames in Hilbert spaces, using discrete bases, is generalized to one where the basis vectors may be labelled using discrete, continuous, or a mixture of the two types of indices. A comprehensive analysis of such frames is presented and various notions of equivalence among frames are introduced. A consideration of the relationschip between reproducing kernel Hilbert spaces and frames leads to an exhaustive construction for all possible frames in a separable Hilbert space. Generalizations of the theory are indicated and illustrated by an example drawn from the afline group. © 1993 Academic Press, Inc.