PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 43(57), pp. 4157 (1988) 

Asymptotic properties of convolution products of functionsE. OmeyEconomische Hogeschool, StAloysius, Brussel, BelgiumAbstract: The asymptotic behaviour of convolution products of the form $\int_0^x f(xy)g(y)\,dy$ is studied. From our results we obtain asymptotic expansions of the form $$ R(x) := \int_o^x f(xy)g(y)\,dy  f(x)\int^\infty g(y)\,dy  g(x)\int_0^\infty f(y)\,dy = O(m(x)). $$ Under rather mild conditions on $f,g$ and $m$ the $O$term can be calculated more explicitly as $$ R(x)(f(x1)f(x))\int_0^\infty yg(y)\,dy+(g(x1) g(x))\int_0^\infty yf(y)\,dy + o(m(x)). $$ An application in probability theory is included. Keywords: convolutions, asymtotic behaviour, subexponential functions, regular variation Classification (MSC2000): 27A12 Full text of the article:
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