, Volume 95, Issue 3, pp 235-239

Convolution quotients of nonnegative functions

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LetG be a locally compact commutative Hausdorff group andf a function belonging toL 1(G). If the integral off with respect to the Haar measure is positive, then one can find a nonnegative (not identically 0) functiong such that the convolution off andg is also nonnegative.