Speaker
Gaétan Leclerc, University of Helsinki
Abstract
The classical Van Der Corput Lemma relates the rate of decay of oscillatory integrals with the concentration of smooth phases near some values. In this talk, we will wonder about “fractal” versions of the Van Der Corput Lemma, where the phases are at most Hölder and highly oscillating. Examples of phases for which Fourier decay statement holds includes Brownian motions and Weierstrass maps. For theses examples, we will see that the less regular the phases, the quicker (!) the oscillatory integral decays. We will then discuss possible generalizations and future projects.
Gaétan Leclerc, University of Helsinki
Abstract
The classical Van Der Corput Lemma relates the rate of decay of oscillatory integrals with the concentration of smooth phases near some values. In this talk, we will wonder about “fractal” versions of the Van Der Corput Lemma, where the phases are at most Hölder and highly oscillating. Examples of phases for which Fourier decay statement holds includes Brownian motions and Weierstrass maps. For theses examples, we will see that the less regular the phases, the quicker (!) the oscillatory integral decays. We will then discuss possible generalizations and future projects.