Uncertainty principles and integral equations associated with a quadratic-phase wavelet transform

Abstract

Taking into account a wavelet transform associated with the quadratic-phase Fourier transform, we obtain several types of uncertainty principles, as well as identify conditions that guarantee the unique solution for a class of integral equations (related with the previous mentioned transforms). Namely, we obtain a Heisenberg–Pauli–Weyl-type uncertainty principle, a logarithmic-type uncertainty principle, a local-type uncertainty principle, an entropy-based uncertainty principle, a Nazarov-type uncertainty principle, an Amrein–Berthier–Benedicks-type uncertainty principle, a Donoho–Stark-type uncertainty principle, a Hardy-type uncertainty principle, and a Beurling-type uncertainty principle for such quadratic-phase wavelet transform. For this, it is crucial to consider a convolution and its consequences in establishing an explicit relation with the quadratic-phase Fourier transform.