Weyl–Bessel transforms

In this work, we define and study the Wigner–Bessel transform and prove for this transform an inversion formula. Next, we use this transform to define the Weyl–Bessel transform Wσ, where σ is a symbol in Sm, m∈R. Using harmonic analysis associated with the Bessel operator, we study criteria in terms of the symbols σ for the boundedness and compactness of the Weyl–Bessel transform Wσ.