Oscillatory Integrals and Fractal Dimension

2016/09/04 by Rolin, Jean-Philippe, Vlah, Domagoj, Zupanovic, Vesna · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1609.00976

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.

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