Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
197-220
Opis fizyczny
Daty
wydano
2014
Twórcy
autor
- Département de Mathématiques Appliquées, Institut Préparatoire aux Études d'Ingénieurs de Nabeul, Université de Carthage, Campus Universitaire, Merazka, 8000, Nabeul, Tunisie
autor
- Université Bordeaux, IMB, UMR 5251, F-33400 Talence, France
- CNRS, IMB, UMR 5251, F-33400 Talence, France
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-sm220-3-1