  In this paper we introduce and investigate the concept of repro- ducing pairs
as a generalization of continuous frames. Reproducing pairs yield a bounded
analysis and synthesis process while the frame condition can be omitted at both
stages. Moreover, we will investigate certain continuous frames (resp.
reproducing pairs) on LCA groups, which can be described as a continuous
version of nonstationary Ga- bor systems and state sufficient conditions for
these systems to form a continuous frame (resp. reproducing pair). As a
byproduct we iden- tify the structure of the frame operator (resp. resolution
operator). We will apply our results to systems generated by a unitary action
of a subset of the affine Weyl-Heisenberg group in $L^2(\mathbb{R})$. This
setup will also serve as a nontrivial example of a system for which, whereas
continuous frames exist, no dual system with the same structure exists even if
we drop the frame property.

Functional Analysis