Localization of Fr\'echet frames and expansion of generalized functions
Abstract
Matrix type operators with the off-diagonal decay of polynomial or sub-exponential types are revisited with weaker assumptions concerning row or column estimates, still giving the continuity results for the frame type operators. Such results are extended from Banach to Fr\'echet spaces. Moreover, the localization of Fr\'echet frames is used for the frame expansions of tempered distributions and a class of Beurling ultradistributions.
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