Affiliation:
1. Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics University of Aveiro Aveiro Portugal
2. Center for Mathematics of the University of Coimbra (CMUC), Department of Mathematics University of Coimbra Coimbra Portugal
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.
Funder
Center for Research and Development in Mathematics and Applications
Subject
General Engineering,General Mathematics