Nazarov's uncertainty principles in higher dimension

2006/12/13 by Philippe Jaming · 1 citation
Mathematics · #Combinatorics #Dimension (graph theory) #Discrete mathematics #Exponential function #Fourier transform #Function (biology) #Mathematical Analysis and Transform Methods #Mathematical analysis #Mathematical functions and polynomials #Mathematics #Pure mathematics #Spectral Theory in Mathematical Physics #Translation (biology) #Type (biology) #math.CA #msc:42B10

paper · pdf · doi:10.1016/j.jat.2007.04.005

published as Journal of Approximation Theory (04/05/2007) doi:10.1016/j.jat.2007.04.005

arxiv created 2006/12/13 · openalex publication_date 2007/05/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this paper we prove that there exists a constant C such that, if S,Σ are subsets of \R^d of finite measure, then for every function f∈ L²(\R^d), ∫_\R^d|f(x)|² dx ≤ C e^C min(|S||Σ|, |S|^1/dw(Σ), w(S)|Σ|^1/d) (∫_{\R^d∖ S}|f(x)|² dx + ∫_\R^d∖Σ|f(x)|² dx) where f is the Fourier transform of f and w(Σ) is the mean width of Σ. This extends to dimension d≥ 1 a result of Nazarov \citepp.Na in dimension d=1.

Citations

• The uncertainty principle: A mathematical survey
• The Uncertainty Principle

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