Uncertainty principles for integral operators

• Autorzy: Saifallah Ghobber , Philippe Jaming
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42C20: Other transformations of harmonic type

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 220
• Numer: 3
• Strony: 197-220

Daty

wydano

2014

Twórcy

autor

Saifallah Ghobber

• Département de Mathématiques Appliquées, Institut Préparatoire aux Études d'Ingénieurs de Nabeul, Université de Carthage, Campus Universitaire, Merazka, 8000, Nabeul, Tunisie

autor

Philippe Jaming

• Université Bordeaux, IMB, UMR 5251, F-33400 Talence, France
• CNRS, IMB, UMR 5251, F-33400 Talence, France

Identyfikatory

DOI

10.4064/sm220-3-1