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Microlocal analysis of generalized functions: pseudodifferential techniques and propagation of singularities
journal contribution
posted on 2015-04-17, 14:09 authored by Claudia Garetto, Gunther HormannWe characterize microlocal regularity, in the script G sign ∞-sense, of Colombeau generalized functions by an appropriate extension of the classical notion of micro-ellipticity to pseudodifferential operators with slow-scale generalized symbols. Thus we obtain an alternative, yet equivalent, way of determining generalized wavefront sets that is analogous to the original definition of the wavefront set of distributions via intersections over characteristic sets. The new methods are then applied to regularity theory of generalized solutions of (pseudo)differential equations, where we extend the general non-characteristic regularity result for distributional solutions and consider propagation of script G sign ∞-singularities for homogeneous first-order hyperbolic equations.
History
School
- Science
Department
- Mathematical Sciences
Published in
Proceedings of the Edinburgh Mathematical SocietyVolume
48Issue
3Pages
603 - 629Citation
GARETTO, C. and HORMANN, G., 2005. Microlocal analysis of generalized functions: pseudodifferential techniques and propagation of singularities. Proceedings of the Edinburgh Mathematical Society (Series 2), 48 (3), pp. 603 - 629.Publisher
Cambridge University Press / © Edinburgh Mathematical SocietyVersion
- SMUR (Submitted Manuscript Under Review)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2005Notes
This paper was published in the journal, Proceedings of the Edinburgh Mathematical Society [Cambridge University Press / © Edinburgh Mathematical Society]. The definitive version is available at: http://dx.doi.org/10.1017/S0013091504000148ISSN
0013-0915Publisher version
Language
- en