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The paper is devoted to frame expansions in Fr\'echet spaces. First we reviewsome results which concern series expansions in general Fr\'echet spaces viaFr\'echet and General Fr\'echet frames. Then we present some new results onseries expansions of tempered distributions and ultradistributions, and thecorresponding test functions, via localized frames and coefficients inappropriate sequence spaces.

Frame expansions of test functions, tempered distributions, and ultradistributions