Let P be a probability distribution defined on the Borel sets of the real line. Suppose that P is symmetric with respect to the origin, absolutely continuous with respect to the Lebesgue measure, and its density function p is zero outside the interval [\minus{}1,1] and inside this interval it is between the positive numbers c and d (c<d). Prove that there is no distribution whose convolution square equals P.
T. F. Mori, G. J. Szekely probabilityreal analysisfunctionSupportintegrationcomplex numbersprobability and stats