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Keywords:

  • Real analytic functions;
  • convolution operator;
  • surjectivity;
  • right inverse MSC (2010) Primary: 35R50;
  • Secondary: 26E05;
  • 46F15;
  • 46M18

Abstract

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) [RIGHTWARDS ARROW] 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.