New uncertainty principles for the $(k,a)$-generalized wavelet transform
We present the basic $(k,a)$-generalized wavelet theory and prove several Heisenberg-type inequalities for this transform. After reviewing Pitt's and Beckner's inequalities for the $(k,a)$-generalized Fourier transform, we connect both inequalities to show a generalization of uncertainty principles for the $(k,a)$-generalized wavelet transform. We also present two concentration uncertainty principles, namely the Benedicks–Amrein–Berthier's uncertainty principle and local uncertainty principles. Finally, we connect these inequalities to show a generalization of the uncertainty principle of Heisenberg type and we prove the Faris–Price uncertainty principle for the $(k,a)$-generalized wavelet transform.
Copyright (c) 2022 Hatem Mejjaoli
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal. The Journal may retract the paper after publication if clear evidence is found that the findings are unreliable as a result of misconduct or honest error.