Convolution of radius functions on ℝ³

Konstanty Holly

Annales Polonici Mathematici (1994)

  • Volume: 60, Issue: 1, page 1-32
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Konstanty Holly. "Convolution of radius functions on ℝ³." Annales Polonici Mathematici 60.1 (1994): 1-32. <http://eudml.org/doc/262496>.

@article{KonstantyHolly1994,
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.},
author = {Konstanty Holly},
journal = {Annales Polonici Mathematici},
keywords = {integral formulas; asymptotic behaviour of convolution at ∞; asymptotic behaviour of convolutions at ; convolution of radius functions; velocity; pressure; fluid; Navier-Stokes equations},
language = {eng},
number = {1},
pages = {1-32},
title = {Convolution of radius functions on ℝ³},
url = {http://eudml.org/doc/262496},
volume = {60},
year = {1994},
}

TY - JOUR
AU - Konstanty Holly
TI - Convolution of radius functions on ℝ³
JO - Annales Polonici Mathematici
PY - 1994
VL - 60
IS - 1
SP - 1
EP - 32
AB - 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.
LA - eng
KW - integral formulas; asymptotic behaviour of convolution at ∞; asymptotic behaviour of convolutions at ; convolution of radius functions; velocity; pressure; fluid; Navier-Stokes equations
UR - http://eudml.org/doc/262496
ER -

References

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  1. [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. Zbl0749.35033
  2. [2] K. Holly, Navier-Stokes equations in ℝ³: relations between pressure and velocity, Internat. Conf. 'Nonlinear Differential Equations', Varna 1987, unpublished. 
  3. [3] N. S. Landkof, Foundations of Modern Potential Theory, Nauka, Moscow, 1966 (in Russian). Zbl0253.31001
  4. [4] M. Riesz, Intégrales de Riemann-Liouville et potentiels, Acta Sci. Math. (Szeged) 9 (1938), 1-42. Zbl64.0476.03

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