Real analytic dependence of simple and double layer potentials for the Helmholtz equation upon perturbationof the support and of the density

We consider a hypersurface in Eucledian space ${\mathbb{R}}^{n}$ parametrized by a diffeomorphism of the boundary of a regular domain in ${\mathbb{R}}^{n}$ to ${\mathbb{R}}^{n}$, and a density function on the hypersurface, which we think as points in suitable Schauder spaces, and a fundamental solution of the Helmholtz equation. Then we investigate the dependence of the corresponding simple and double layer potentials, which we also think as points in suitable Schauder spaces, upon variation of the diffeomorphism and of the density and of the wave number of the Helmholtz equation, and we show a real analyticity theorem for such dependence, thus extending the validity of a result of R.~Potthast.