Some remarks on stable densities and operators of fractional differentiation

Abstract

Let $D(s)$ be a fractional derivation of order $s$. For a real $p\ne 0$, we construct an integral operator $A(p)$ in an appropriate functional space such that $A(p)D(s)A(p{)}^{-1}=D(ps)$ for all $s$. The kernel of the operator $A(p)$ is expressed in terms of a function similar to the stable densities.

References in corpus (1)

• Plancherel formula for Berezin deformation of $L^2$ on Riemannian symmetric space