Khaled Hleili

L^p Uncertainty Principles for the Windowed Spherical Mean Transform

abstract:
In this work, we establish the $L^p$ local uncertainty principle for the windowed spherical mean transform and deduce the $L^p$ version of the Heisenberg-Pauli-Weyl uncertainty principle. Finally, using the previous uncertainty principles and the techniques of Donoho-Stark, we present uncertainty principles of concentration type in the $L^p$ theory, when $1<p\leqslant2$.

Mathematics Subject Classification: 42B10, 44A05

Key words and phrases: Windowed Fourier transform, local uncertainty principles, Heisenberg-Pauli-Weyl inequality, concentration uncertainty principles