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Microlocal analysis of ultradistributions
Author(s):
Stevan
Pilipovic
Journal:
Proc. Amer. Math. Soc.
126
(1998),
105-113.
MSC (1991):
Primary 32A40, 46F15;
Secondary 58G07
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Abstract:
The ultradistributional wave front sets of an ultradistribution are characterized by the behaviour of on the boundary of the tube domain , where is the kernel analysed by Hörmander.
References:
- 1.
- A. Eida, On the microlocal decomposition of ultradistributions and ultradifferentiable functions, Preprint.
- 2.
- L. Hörmander, The Analysis of Linear Partial Differential Operators I, Springer, Berlin - Heidelberg - New York - Tokyo, 1983. MR 91m:35001b
- 3.
- H. Komatsu, Ultradistributions, I - III, J. Fac. Sci. Univ. Tokyo, Sect. IA 20(1973), 25-105; 24(1977) 607 - 628; 29(1982), 653 - 717. MR 47:9277; MR 57:17280; MR 84d:46051
- 4.
- H. Komatsu, Microlocal Analytic in Gevrey Classes and in Convex Domains, Springer, Lec. Not. Math. 1726(1989), 426 - 493.
- 5.
- D. Kova\v{c}evi\'{c}, S. Pilipovi\'{c}, Structural properties of the spaces of tempered ultradistributions, Proc. Conf. ``Complex Analysis and Generalized Functions", Varna 1991, 169 - 184. MR 95c:46059
- 6.
- H. J. Petzsche, Generalized functions and the boundary values of holomorphic functions, J. Fac. Sci. Univ. Tokyo, Sect. IA Math. 31 (1984), 391-431. MR 85k:46048
- 7.
- S. Pilipovi\'{c}, Characterization of bounded sets in spaces of ultradistributions, Proc. AMS, 120(1994), 1191-1206. MR 94f:46048
- 8.
- S. Pilipovi\'{c}, Structural Theorems for Ultradistributions, Ann. Polon. Math. 340(1995), 223-235. MR 96f:46076
- 9.
- J. W. de Roewer, Hyperfunctional singular support of distributions, J. Fasc. Sci. Univ. Tokyo, Sec IA Math. 31(1985), 585 - 631. MR 86d:46039
- 10.
- M. Sato, T. Kawai, M. Kashiwara, Microfunctions and Pseudo - differential Equations, Springer, Lect. Not. Math. 287 (1973), 265-529. MR 54:8747
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Additional Information:
Stevan
Pilipovic
Affiliation:
Institute of Mathematics, University of Novi Sad, Trg D. Obradovica 4, 21000 Novi Sad, Yugoslavia
DOI:
10.1090/S0002-9939-98-04357-3
PII:
S 0002-9939(98)04357-3
Keywords:
Ultradistributions,
wave front
Received by editor(s):
February 27, 1996
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1998,
American Mathematical Society
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