Geophysical modelling with Colombeau functions: Microlocal properties and Zygmund regularity
Analysis of PDEs
2007-05-23 v3 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.math/0104007,
title = {Geophysical modelling with Colombeau functions: Microlocal properties and Zygmund regularity},
author = {G. Hoermann and M. V. de Hoop},
journal= {arXiv preprint arXiv:math/0104007},
year = {2007}
}
Comments
corrected Definition 13; updated Remark 5