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Title: Microlocal analysis of generalized functions: pseudodifferential techniques and propagation of singularities
Authors: Garetto, Claudia
Hormann, Gunther
Keywords: Algebras of generalized functions
Pseudodifferential operators
Wavefront sets
Issue Date: 2005
Publisher: Cambridge University Press / © Edinburgh Mathematical Society
Citation: 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.
Abstract: We 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.
Description: 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/S0013091504000148
Version: Submitted for publication
DOI: 10.1017/S0013091504000148
URI: https://dspace.lboro.ac.uk/2134/17302
Publisher Link: http://dx.doi.org/10.1017/S0013091504000148
ISSN: 0013-0915
Appears in Collections:Published Articles (Maths)

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