Abstract
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.
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