Communications of the
Korean Mathematical Society CKMS

In this paper, we introduce the k-Hankel-Wigner transform on $mathbb{R}$ in some problems of time-frequency analysis. As a first point, we present some harmonic analysis results such as Plancherel's, Parseval's and an inversion formulas for this transform. Next, we prove a Heisenberg's uncertainty principle and a Calder'on's reproducing formula for this transform. We conclude this paper by studying an extremal function for this transform.

Keywords: k-Hankel transform, k-Hankel-Wigner transform, Plancherel's formula, Heisenberg's uncertainty principle, Calder'on's reproducing formula, extremal function

MSC numbers: Primary 42B10, 44A20, 46F12