The ultrahyperbolic Bessel operator: An inversion theorem

In this note, we prove that the two following conclusions are equivalent: for ƒ and ϑ temperate distributions, ƒ = Bαϑ and ϑ = limϵ→0Dϵα ƒ (cf., Theorem 3.3, formulas (3.17) and (3.18)). Here, Dϵαƒ is the truncated Bessel derivative of order α and Bαϑ is the ultrahyperbolic Bessel operator defined by formulas (1.15) and (1.16), respectively. Here, we generalize an article due to B.S. Rubin (cf., [1]).