most citedOscillatory Integral Decay, Sublevel Set Growth, and the Newton Polyhedron

1 citations · 1 across the 3 of their papers we have counts for

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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…