Oscillatory Integrals and Fractal Dimension
Classical Analysis and ODEs
2016-09-22 v2
Abstract
We study geometrical representation of oscillatory integrals with an analytic phase function and a smooth amplitude with compact support. Geometrical properties of the curves defined by the oscillatory integral depend on the type of a critical point of the phase. We give explicit formulas for the box dimension and the Minkowski content of these curves. Methods include Newton diagrams and the resolution of singularities.
Cite
@article{arxiv.1609.00976,
title = {Oscillatory Integrals and Fractal Dimension},
author = {Jean-Philippe Rolin and Domagoj Vlah and Vesna Zupanovic},
journal= {arXiv preprint arXiv:1609.00976},
year = {2016}
}