Regularity properties of distributions through sequences of functions
classification
🧮 math.FA
keywords
functionssequencessmoothtermsapproximationarisingcontinuouscriteria
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We give necessary and sufficient criteria for a distribution to be smooth or uniformly H\"{o}lder continuous in terms of approximation sequences by smooth functions; in particular, in terms of those arising as regularizations $(T\ast\phi_{n})$.
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