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.
@article{bwmeta1.element.bwnjournal-article-apmv60z1p1bwm,
author = {Konstanty Holly},
title = {Convolution of radius functions on $\mathbb{R}$$^3$},
journal = {Annales Polonici Mathematici},
volume = {60},
year = {1994},
pages = {1-32},
zbl = {0869.42008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv60z1p1bwm}
}
Konstanty Holly. Convolution of radius functions on ℝ³. Annales Polonici Mathematici, Tome 60 (1994) pp. 1-32. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv60z1p1bwm/
[000] [1] K. Holly, Navier-Stokes equations in ℝ³ as a system of nonsingular integral equations of Hammerstein type. An abstract approach, Univ. Iagel. Acta Math. 28 (1991), 151-161. | Zbl 0749.35033
[001] [2] K. Holly, Navier-Stokes equations in ℝ³: relations between pressure and velocity, Internat. Conf. 'Nonlinear Differential Equations', Varna 1987, unpublished.
[002] [3] N. S. Landkof, Foundations of Modern Potential Theory, Nauka, Moscow, 1966 (in Russian). | Zbl 0253.31001
[003] [4] M. Riesz, Intégrales de Riemann-Liouville et potentiels, Acta Sci. Math. (Szeged) 9 (1938), 1-42. | Zbl 64.0476.03