Given any finite direction set $\Omega$ of cardinality $N$ in Euclidean space, we consider the maximal directional Hilbert transform $H_{\Omega}$ associated to this set. Our main result provides an essentially sharp uniform bound, depending only on $N$, for $L^2$ operator norm dimensions 3 and higher. The ingredients proof consist polynomial partitioning tools from incidence geometry almost-ort...

Estimation of the modal parameters of mechanical systems or structures is usually achieved by applying the well-known Frequency Response Function (FRF) method to experimental data obtained from free vibration after a shock excitation of the system or forced vibration using a variety of excitation signals. This method is however limited only to linear systems. The problem becomes more complex wh...