Directional Time–Frequency Analysis and Directional Regularity

Abstract

© 2017, Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia. We improve some of the results related to the directional short-time Fourier transform by fixing the direction and extend them to the spaces K1(Rn) and K1(R) ⊗ ^ U(Cn) and their duals. Then, we define multidimensional short-time Fourier transform in the direction of uk for tempered distributions, directional regular sets and their complements, directional wave fronts. Different windows with mild conditions on their support show the invariance of these notions related to window functions. Smoothness of f follows from the assumptions of the directional regularity in any direction.