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Microlocal analysis of ultradistributions

Author: Stevan Pilipovic
Journal: Proc. Amer. Math. Soc. 126 (1998), 105-113
MSC (1991): Primary 32A40, 46F15; Secondary 58G07
MathSciNet review: 1451826
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Abstract: The ultradistributional wave front sets of an ultradistribution $u$ are characterized by the behaviour of $K *u$ on the boundary of the tube domain $D \mathbf{R}^n$, where $K$ is the kernel analysed by Hörmander.

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  • 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. Obradovića 4, 21000 Novi Sad, Yugoslavia

Keywords: Ultradistributions, wave front
Received by editor(s): February 27, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society

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