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Characterizations of bounded sets in spaces of ultradistributions

Author: Stevan Pilipović
Journal: Proc. Amer. Math. Soc. 120 (1994), 1191-1206
MSC: Primary 46F05
MathSciNet review: 1211587
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Abstract: We characterize bounded sets in ultradistributions spaces $ \mathcal{D}_{{L^t}}^{'({M_p})},\,t \in [1,\infty ],\,S{'^{\{ {M_p}\} }}$, and $ S{'^{({M_p})}}$ and bounded sets and convergent sequences in $ \mathcal{D}{'^{({M_p})}}$ and $ \mathcal{D}{'^{\{ {M_p}\} }}$ via the convolution by corresponding test functions. The structural theorems for $ \mathcal{D}_{{L^t}}^{'\{ {M_p}\} }$ and $ \widetilde D_{{L^t}}^{'\{ {M_p}\} },\;t \in [1,\infty ]$, are also given.

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