A multi-dimensional resolution of singularities with applications to analysis
Classical Analysis and ODEs
2011-08-09 v2
Abstract
We formulate a resolution of singularities algorithm for analyzing the zero sets of real-analytic functions in dimensions . Rather than using the celebrated result of Hironaka, the algorithm is modeled on a more explicit and elementary approach used in the contemporary algebraic geometry literature. As an application, we define a new notion of the height of real-analytic functions, compute the critical integrability index and obtain the sharp growth rate of sublevel sets. This also leads to a characterization of the oscillation index of scalar oscillatory integrals with real-analytic phases in all dimensions.
Cite
@article{arxiv.1007.0519,
title = {A multi-dimensional resolution of singularities with applications to analysis},
author = {Tristan Collins and Allan Greenleaf and Malabika Pramanik},
journal= {arXiv preprint arXiv:1007.0519},
year = {2011}
}