ON BESSEL-RIESZ OPERATORS

Abstract

We consider a class of conv olution operator denoted ϕα W obtained by convolution with a generalized function expressible in terms of the Bessel function on first kind γ J with argument the distribution ( ) P ± i0 . We study some elementary properties of the operator ϕα W like the semigroup property ϕ = ϕ α β α+β W W W ; and ( +m2 ) α α−2 W ϕ = W for α > 2 where ( +m2 ) is the Klein-Gordon ultrahyperbolic operator. Moreover we prove that the operator ϕα W may be consider as a negative power of the Klein-Gordon operato