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(12):8447–8480. 
Bibtex entry
@ARTICLE { MR3551577,
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 },
VOLUME = { 368 },
YEAR = { 2016 },
NUMBER = { 12 },
PAGES = { 8447--8480 },
ISSN = { 0002-9947 },
MRCLASS = { 42C15 (43A32 43A60 43A70 46C05) },
MRNUMBER = { 3551577 },
MRREVIEWER = { Georg Berschneider },
DOI = { 10.1090/tran/6594 },
URL = { https://doi.org/10.1090/tran/6594 },
}