| Abstrakt: |
Time-frequency localization operators (with Gaussian window) L_F:L^2(\mathbb {R}^d)\to L^2(\mathbb {R}^d), where F is a weight in \mathbb {R}^{2d}, were introduced in signal processing by I. Daubechies [IEEE Trans. Inform. Theory 34 (1988), pp. 605–612], inaugurating a new, geometric, phase-space perspective. Sharp upper bounds for the norm (and the singular values) of such operators turn out to be a challenging issue with deep applications in signal recovery, quantum physics and the study of uncertainty principles. In this note we provide optimal upper bounds for the operator norm \|L_F\|_{L^2\to L^2}, assuming F\in L^p(\mathbb {R}^{2d}), 1
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