Strong annihilating pairs for the Fourier–Bessel transform

By Saifallah Ghobber, Philippe Jaming. 2010

48 citations recorded by the source corpus.

Abstract The aim of this paper is to prove two new uncertainty principles for the Fourier–Bessel transform (or Hankel transform). The first of these results is an extension of a result of Amrein, Berthier and Benedicks, it states that a non-zero function f and its Fourier–Bessel transform F α ( f ) cannot both have support of finite measure. The second result states that the supports of f and F α ( f ) cannot both be ( e , α ) -thin, this extending a result of Shubin, Vakilian and Wolff. As a side result we prove that the dilation of a C 0 -function are linearly independent. We also extend Faris's local uncertainty principle to the Fourier–Bessel transform.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/84b3eec5a6120f60e55687547851be532a892acb

How researchers see this paper

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In Applied Mathematics

1. Saifallah Ghobber
2. Philippe Jaming
3. Slim Omri
4. Eugenia Malinnikova

In Mathematical Physics

1. Saifallah Ghobber
2. Philippe Jaming

Citations in the corpus

• Uncertainty principles for integral operators (2012, methodology): “Before proving our main theorem, we will now prove the following lemma which results directly from a similar result in [25] for functions in C0(R).”
• Time–frequency concentration of the windowed Hankel transform (2014, background): “The extension of the result of Benedicks–Amrein–Berthier for the Hankel transform is shown in [11] and its corresponding version for the windowed Fourier transform is given independently in [5,7,12,13], namely for a non-zero window function g ∈ L2(Rd) and for a subset ∈ Rd × R̂d of finite Lebesgue m”