Geophysical modelling with Colombeau functions: Microlocal properties and Zygmund regularity

Details Geophysical modelling with Colombeau functions: Microlocal properties and Zygmund regularity Geophysical modelling with Colombeau functions: Microlocal properties and Zygmund regularity

2001-03-31

arxiv.org/abs/math/0104007v3

Mathematics

Analysis of PDEs

corrected Definition 13; updated Remark 5

Scientific paper

In global seismology Earth's properties of fractal nature occur. Zygmund classes appear as the most appropriate and systematic way to measure this local fractality. For the purpose of seismic wave propagation, we model the Earth's properties as Colombeau generalized functions. In one spatial dimension, we have a precise characterization of Zygmund regularity in Colombeau algebras. This is made possible via a relation between mollifiers and wavelets.

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