Directional time-frequency analysis and directional regularity (Q2272612)

The authors introduce a multidimensional variant of the directional short-time Fourier transform and employ it to define a multidirectional wave front set of a tempered distribution. They prove that these wave front sets do not depend on the windows and that the smoothness of \(f\in\mathcal{S}'(\mathbb{R}^n)\) follows from its directional regularity in any direction.