| Publication type: |
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Preprint, Working Paper, ... |
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| Subject: |
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Mathematics/Classical Analysis and ODEs
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| Title: |
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Uncertainty principles for integral operators |
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| Author(s): |
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Saifallah Ghobber ( ) 1, 2, Philippe Jaming (,  ) 3 |
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| Laboratory: |
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| Abstract: |
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The aim of this paper is to prove new uncertainty principles for an integral operator $\tt$ with a 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 $f\in L^2(\R^d,\mu)$ is highly localized near a single point then $\tt (f)$ 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 $f\in L^2(\R^d,\mu)$ and its integral transform $\tt (f)$ cannot both have support of finite measure. From these two results we deduce a global uncertainty principle of Heisenberg type for the transformation $\tt$. We apply our results to obtain a new uncertainty principles for the Dunkl and Clifford Fourier transforms. |
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| Fulltext language: |
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English |
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| Production date: |
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2012-06 |
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| Keyword(s): |
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Uncertainty principles – annihilating pairs – Dunkl transform – Fourier-Clifford transform – integral operators |
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| Classification: |
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42A68;42C20 |
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