Uncertainty principles for the multidimensional quadratic-phase Fourier transform

Abstract Taking into account the recently introduced multidimensional quadratic-phase Fourier transform, which has made it possible to analyse various generalizations of the Fourier transform, also in a multidimensional context, the main objective of this research is to obtain different uncertainty principles for this new global integral transform. It is in this context that e.g. Heisenberg, Nazarov, Hardy, Morgan, Beurling, Pitt, logarithmic, entropy, Amrein-Berthier-Benedicks and local type uncertainty principles for the multidimensional quadratic-phase Fourier transform are deduced here. We also obtain a Hausdorff-Young inequality with Beckner’s constant for the multidimensional quadratic-phase Fourier transform and deduce some of its consequences.