a1 Department of Pure Mathematics and Mathematical Statistics, McGill University, Montreal H3A 2K6, Canada
a2 Department of Mathematics, Southwest Missouri State University, Springfield, Missouri 65809, U.S.A.
Let ƒ be a smooth function of compact support defined in the plane and consider the integral
is well-known, see for instance the work of Littman. The operator T amounts to convolution with the measure σ carried by the parabola t → (t, ½t2) and given by dσ = dt. Usually one proves (1) by embedding σ in an analytic family of distributions σz in 2 given by
(Received September 03 1990)
(Revised January 30 1991)