Convolution operators on spaces of real analytic functions

摘要

Let I {is contained in} R be an open interval and let μ ∈ A(R)' and G:= conv(supp(μ)). We characterize the surjectivity of the convolution operator Tμ: A(I - G) → A(I) by means of a new estimate from below for the Fourier transform μ{top}^ valid on conical subsets of C/R. We also characterize when Tμ admits a continuous linear right inverse.