Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] I. Cioranescu, The characterization of the almost-periodic ultradistributions of Beurling type, Proc. Amer. Math. Soc. 116 (1992), 127-134. MR 1111214 (92k:46063)
  • [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] J. Harvat, Topological vector spaces and distributions, Addison-Wesley, Reading, MA, 1966. MR 0193469 (33:1689)
  • [4] H. Komatsu, Ultradistributions, I: Structure theorems and a characterization, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 20 (1973), 23-105. MR 0320743 (47:9277)
  • [5] -, Ultradistributions, III: Vector valued ultradistributions and the theory of kernels, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 29 (1982), 653-718. MR 687595 (84d:46051)
  • [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] H. J. Patzsche, Generalized functions and the boundary values of holomorphic function, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 31 (1984), 391-431. MR 763428 (85k:46048)
  • [10] S. Pilipović, Tempered ultradistributions, Boll. Un. Mat. Ital. B 2 (1988), 235-251. MR 946067 (89f:46088)
  • [11] -, On the convolution in the space of Beurling ultradistributions, Comm. Math. Univ. St. Pauli 40 (1991), 15-27. MR 1104777 (92e:46086)
  • [12] L. Schwartz, Theorie des distributions. I, II, 2nd ed., Hermann, Paris, 1966. MR 0209834 (35:730)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46F05

Retrieve articles in all journals with MSC: 46F05


Additional Information

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

American Mathematical Society