Oscillatory integrals and fractal dimension

Jean-Philippe Rolin (1) , Domagoj Vlah (2) , Vesna Županović (2)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 FER - Faculty of Electrical Engineering and Computing [Zagreb]

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.

Mots clés: Oscillatory integral; Box dimension; Minkowski content; Critical points; Newton diagram

Domaines: Mathématiques [math]

Jean-Philippe Rolin, Domagoj Vlah, Vesna Županović. Oscillatory integrals and fractal dimension. Bulletin des Sciences Mathématiques, 2021, 168, pp.102972. ⟨10.1016/j.bulsci.2021.102972⟩. ⟨hal-03301363⟩