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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
DOI: https://doi.org/10.1090/S0002-9939-1994-1211587-0
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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  • [1] Ioana Cioranescu, The characterization of the almost periodic ultradistributions of Beurling type, Proc. Amer. Math. Soc. 116 (1992), no. 1, 127–134. MR 1111214, https://doi.org/10.1090/S0002-9939-1992-1111214-5
  • [2] I. M. Gelfand and G. E. Shilov, Generalized function, Vol. 2, Spaces of Fundamental and Generalized Functions, Academic Press, New York and London, 1968.
  • [3] Helmut H. Schaefer, Topological vector spaces, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1966. MR 0193469
  • [4] Hikosaburo Komatsu, Ultradistributions. I. Structure theorems and a characterization, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 20 (1973), 25–105. MR 0320743
  • [5] Hikosaburo Komatsu, Ultradistributions. III. Vector-valued ultradistributions and the theory of kernels, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 29 (1982), no. 3, 653–717. MR 687595
  • [6] -, Microlocal analysis in Gevrey class and complex domains, UTYO-MATH 91-15 (1991), Lecture delivered at CIME, Inter. Math. Summer Institute: Mycrolocal Analysis and Applications, Montecatini, 1989 (to appear in Lecture Notes).
  • [7] D. Kovačević and S. Pilipović, Structural properties of the space of tempered ultradistributions, Proc. Conf. Complex Analysis and Application '91 with Symposium on Generalized functions (Varna, 1991) (to appear).
  • [8] -, Integral transformations of tempered ultradistributions, preprint.
  • [9] Hans-Joachim Petzsche, Generalized functions and the boundary values of holomorphic functions, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 31 (1984), no. 2, 391–431. MR 763428
  • [10] Stevan Pilipović, Tempered ultradistributions, Boll. Un. Mat. Ital. B (7) 2 (1988), no. 2, 235–251 (English, with Italian summary). MR 946067
  • [11] S. Pilipović, On the convolution in the space of Beurling ultradistributions, Comment. Math. Univ. St. Paul. 40 (1991), no. 1, 15–27. MR 1104777
  • [12] Laurent Schwartz, Théorie des distributions, Publications de l’Institut de Mathématique de l’Université de Strasbourg, No. IX-X. Nouvelle édition, entiérement corrigée, refondue et augmentée, Hermann, Paris, 1966 (French). MR 0209834

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DOI: https://doi.org/10.1090/S0002-9939-1994-1211587-0
Article copyright: © Copyright 1994 American Mathematical Society