A variant of the Hankel multiplier. (English) Zbl 1383.81120

Ghobber, Saifallah

Banach J. Math. Anal. 12, No. 1, 144-166 (2018).

Summary: The first aim of this article is to survey and revisit some uncertainty principles for the Hankel transform by means of the Hankel multiplier. Then we define the wavelet Hankel multiplier and study its boundedness and Schatten-class properties. Finally, we prove that the wavelet Hankel multiplier is unitary equivalent to a scalar multiple of the phase space restriction operator, for which we deduce a trace formula.

MSC:

81S30	Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
94A12	Signal theory (characterization, reconstruction, filtering, etc.)
45P05	Integral operators
42C25	Uniqueness and localization for orthogonal series
42C40	Nontrigonometric harmonic analysis involving wavelets and other special systems
62J10	Analysis of variance and covariance (ANOVA)

Keywords:

Hankel multiplier; localization operator; uncertainty principle; Nash inequality; Carlson inequality