AN ALTERNATIVE METHOD FOR THE ASYMPTOTIC-EXPANSION OF A DOUBLE INTEGRAL

An alternative method is proposed in order to obtain, as lambda --> +i nfinity , the asymptotic expansion of the double integral K(lambda) := integral(0)(1) integral(0)(1) [x(alpha)y(beta) log' x log' y]f(x, y)g (lambda x(a)y(b)) dx dy, where fis smooth enough and g belongs to A(R) , a space defined in the text. This expansion is derived by employing a powerful tool - the integration in the finite-part sense of Hadamard . (C) 1995 Academic Press. Inc.