On Hankel Convolution Equations in Distribution Spaces

Hypoellipticity of Hankel convolution equations on Schwartz distribution spaces

“…The study of Hankel convolution equations on distributions of slow growth and of exponential growth was developed in [4] and [7]. In this paper we analyze the hypoellipticity of Hankel convolution equations defined by elements of E * in the space D * .…”

On the surjectivity of Hankel convolution operators on Beurling-type distribution spaces

“…In this section we present necessary and sufficient conditions on a distribution S ∈ E(w) in order that B(w) #S = B(w) , that is, for every R ∈ B(w) there exists T ∈ B(w) for which T #S = R. Solvability of Hankel convolution equations in Zemanian distribution spaces was studied in [7], and on distribution with exponential growth in [9]. We now establish our main result.…”

Hypoellipticity of Hankel Convolution Equations in DL1-Type Spaces

“…Assume now that S ∈ H µ,∞ . To see that |a j | = o(ξ n j ), as j → ∞, for every n ∈ N, we proceed as in the proof of [6,Proposition 3.2]. Let k ∈ N and φ ∈ S e .…”

“…where x, y ∈ [0, ∞) and f, g ∈ L 1 (x 2µ+1 dx). The Hankel convolution was studied in distribution spaces in [5], [6] and [12]. In the sequel, to simplify we will write #, τ x , x ∈ [0, ∞), and D, instead # µ , µ τ x , x ∈ [0, ∞), and D µ , respectively.…”