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Published
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New uncertainty principles for the $(k,a)$-generalized wavelet transform
Volume 63, no. 1
(2022),
pp. 239–279
https://doi.org/10.33044/revuma.2051
Abstract
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.
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Published by the Unión Matemática Argentina |
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