# Convolution of radius functions on ℝ³

Annales Polonici Mathematici (1994)

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

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 'Nonlinear Differential Equations', Varna 1987, unpublished.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

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