On the n-dimensional Hankel transforms of arbitrary order

Abstract

In S.E. Trione and S. Molina, The n-dimensional Hankel transform and complex powers of Bessel operator, to appear in Integral Transforms and Spec. Funct. we study a version of the n-dimensional Hankel transform h μ for μ=(μ1, …, μ n )∈ℝ n and μ i ≥−1/2 for all i. In this paper, we extend the n-dimensional Hankel transform to arbitrary values of μ∈ℝ n . Moreover, we obtain some results for the inverse of this extension.