Geophysical modelling with Colombeau functions: Microlocal properties and Zygmund regularity

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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.
corrected Definition 13; updated Remark 5

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Analysis of PDEs, Mathematical Physics, 46F30; 35D10

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http://salesiana.dossiersoluciones.com/handle/123456789/61200

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0104007
 http://arxiv.org/abs/math/0104007

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arXiv