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Convolution operators on spaces of real analytic functions


  • Dedicated to Professor Dr. D. Vogt on the occasion of his 70th birthday


Let equation image be an open interval and let equation image and equation image. We characterize the surjectivity of the convolution operator Tμ: A(IG) → A(I) by means of a new estimate from below for the Fourier transform equation image valid on conical subsets of equation image. We also characterize when Tμ admits a continuous linear right inverse.