Convolution of radius functions on ℝ³

Konstanty Holly

Annales Polonici Mathematici (1994)

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

Abstract

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.