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Uncertainty principles for integral operators

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Ghobber S., Jaming P.

Studia Mathematica

2014

tom 220

nr 3

197-220

The aim of this paper is to prove new uncertainty principles for integral operators 𝓣 with bounded kernel for which there is a Plancherel Theorem. The first of these results is an extension of Faris's local uncertainty principle which states that if a nonzero function $f ∈ L²(ℝ^{d},μ)$ is highly localized near a single point then 𝓣(f) cannot be concentrated in a set of finite measure. The second result extends the Benedicks-Amrein-Berthier uncertainty principle and states that a nonzero function $f ∈ L²(ℝ^{d},μ)$ and its integral transform 𝓣(f) cannot both have support of finite measure. From these two results we deduce a global uncertainty principle of Heisenberg type for the transformation 𝓣. We apply our results to obtain new uncertainty principles for the Dunkl and Clifford Fourier transforms.

Ograniczanie wyników

1 Studia Mathematica

1 Ghobber S.

1 Jaming P.

1 2014

Wyniki wyszukiwania

Uncertainty principles for integral operators