Convolution of radius functions on ℝ³
Volume 60 / 1994
Annales Polonici Mathematici 60 (1994), 1-32
DOI: 10.4064/ap-60-1-1-32
Abstract
We reduce the convolution of radius functions to that of 1-variable functions. Then we present formulas for computing convolutions of an abstract radius function on ℝ³ with various integral kernels - given by elementary or discontinuous functions. We also prove a theorem on the asymptotic behaviour of a convolution at infinity. Lastly, we deduce some estimates which enable us to find the asymptotics of the velocity and pressure of a fluid (described by the Navier-Stokes equations) in the boundary layer.
