3 papers
math.CA2009
Resolution of Singularities in Two Dimensions and the Stability of Integrals
Michael Greenblatt
For a small disk D centered at the origin in R^2, a smooth real-valued function S(x,y) on D, and a positive epsilon, we consider the measure of the points in D where |S(x,y)| < eps…
math.CA2008
The asymptotic behavior of degenerate oscillatory integrals in two dimensions
Michael Greenblatt
A theorem of Varchenko gives the order of decay of the leading term of the asymptotic expansion of a degenerate oscillatory integral with real-analytic phase in two dimensions. His…
math.CA2008★ 1 cited
Oscillatory Integral Decay, Sublevel Set Growth, and the Newton Polyhedron
Michael Greenblatt
Using some resolution of singularities methods of the author, a generalization of a well-known theorem of Varchenko relating decay of oscillatory integrals to the Newton polyhedron…