Geodesic
Continuous linear right inverses for convolution operators in spaces of real analytic functions
Studia Mathematica, Tome 110 (1994) no. 1, pp. 65-82

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DOI

We determine the convolution operators $T_μ := μ*$ on the real analytic functions in one variable which admit a continuous linear right inverse. The characterization is given by means of a slowly decreasing condition of Ehrenpreis type and a restriction of hyperbolic type on the location of zeros of the Fourier transform μ̂(z). 
Michael Langenbruch. Continuous linear right inverses for convolution operators in spaces of real analytic functions. Studia Mathematica, Tome 110 (1994) no. 1, pp. 65-82. doi: 10.4064/sm-110-1-65-82
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