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Omri, S.

Logarithmic uncertainty principle for the Hankel transform. (English) Zbl 1227.42010

Integral Transforms Spec. Funct. 22, No. 9, 655-670 (2011).
The author derives several uncertainty principles for the classical Hankel transform. He first proves a sharp Stein-Weiss inequality for Bessel-Riesz potentials. This result is then used to derive analogues of Pitt’s inequality as well as Beckner’s logarithmic uncertainty principle.
Reviewer: Michael Voit (Dortmund)

Cited in 16 Documents

MSC:

42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)

Keywords:

Hankel transform; Stein-Weiss inequality; Riesz potential; logarithmic uncertainty principle; Pitt’s inequality
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References:

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