Pilipović, Stevan Characterizations of bounded sets in spaces of ultradistributions. (English) Zbl 0816.46026 Proc. Am. Math. Soc. 120, No. 4, 1191-1206 (1994). 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. Cited in 29 Documents MSC: 46F05 Topological linear spaces of test functions, distributions and ultradistributions Keywords:Beurling and Roumieau spaces of ultradistributions; bounded sets in ultradistribution spaces PDFBibTeX XMLCite \textit{S. Pilipović}, Proc. Am. Math. Soc. 120, No. 4, 1191--1206 (1994; Zbl 0816.46026) Full Text: DOI