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Characterizations of bounded sets in spaces of ultradistributions. (English) Zbl 0816.46026
Summary: We characterize bounded sets in ultradistribution spaces $${\mathcal D}^{\prime(M_ p)}_{L^ t}$$, $$t\in [1, \infty]$$, $${\mathcal S}^{\prime\{M_ p\}}$$, and $${\mathcal S}^{\prime(M_ p)}$$ and bounded sets and convergent sequences in $${\mathcal D}^{\prime(M_ p)}$$ and $${\mathcal D}^{\prime\{M_ p\}}$$ via the convolution by corresponding test functions. The structural theorems for $${\mathcal D}^{\prime\{M_ p\}}_{L^ t}$$ and $$\widetilde{\mathcal D}^{\prime\{M_ p\}}_{L^ t}$$, $$t\in [1, \infty]$$, are also given.

##### MSC:
 46F05 Topological linear spaces of test functions, distributions and ultradistributions
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