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A reproducing system is a countable collection of functions ${\varphi }_j:j\in$ such that a general function f can be decomposed as $f={\sum }_{j\in }{c}_j\left(f\right){\varphi }_j$, with some control on the analyzing coefficients $c_j\left(f\right)$. Several such systems have been introduced very successfully in mathematics and its applications. We present a unified viewpoint in the study of reproducing systems on locally compact abelian groups G. This approach gives a novel characterization of the Parseval frame generators for a very general class of reproducing systems on L²(G)....