Microlocal Analysis, Time-Frequency Transforms and Local Uncertainty Principles

In this paper we propose an uncertainty principle of local type involving the short-time Fourier transform in the frame of ultradifferentiable spaces.The classical local uncertainty principle for the Fourier transform can be seen as a refinement of the Heisenberg inequality; the results we prove in this paper assert that the L 1 content of a function f in a measurable E must be small as the measure of E is small and/or the ξ-dispersion of the short-time Fourier transform of f is small, giving then a new result related with classical Fourier analysis and time-frequency representations.