The generalized stieltjes and fourier transforms of certain spaces of generalized functions

Abstract EN

Abstract.

Inspired of Roomie and Burling definitions, we defined spaces of ultra-differentiable functions of rapid descents in Lp spaces which shown to be closed with respect to the classical Stilettoes transform.

The generalized Stilettoes transform is thereby defined on the duals through the generalization of the Perceval's equation.

Further, we obtained spaces and derived certain related results justifying multiplication.

Adopting the concept of Bohemian spaces, the celebrated Fourier transforms were extended to a so-called space of ultra-differentiable Bohemians.