Summary
Mads Sielemann Jakobsen and Jakob Lemvig (2016) Reproducing formulas for generalized translation invariant systems on locally compact abelian groups. Trans. Amer. Math. Soc., 368:8447–8480. 
Bibtex entry
@ARTICLE { Lemvig14Reproducing,
AUTHOR = { Mads Sielemann Jakobsen and Jakob Lemvig },
TITLE = { Reproducing formulas for generalized translation invariant systems on locally compact abelian groups },
JOURNAL = { Trans. Amer. Math. Soc. },
FJOURNAL = { Transactions of the American Mathematical Society },
YEAR = { 2016 },
VOLUME = { 368 },
PAGES = { 8447--8480 },
URL = { http://dx.doi.org/10.1090/tran/6594 },
DOR = { 10.1090/tran/6594 },
PDF = { /lemvig_14.pdf },
TAG = { journal },
}