Geodesic
Finding Solution Subspaces of the Laplace and Heat Equations
Matematičeskie zametki, Tome 103 (2018) no. 6, pp. 803-817

Voir la notice de l'article provenant de la source Math-Net.Ru

We single out subspaces of harmonic functions in the upper half-plane coinciding with spaces of convolutions with the Abel–Poisson kernel and subspaces of solutions of the heat equation coinciding with spaces of convolutions with the Gauss–Weierstrass kernel that are isometric to the corresponding spaces of real functions defined on the set of real numbers. It is shown that, due to isometry, the main approximation characteristics of functions and function classes in these subspaces are equal to the corresponding approximation characteristics of functions and function classes of one variable.
Mots-clés : Laplace equation, Abel–Poisson delta kernel, Gauss–Weierstrass delta kernel, heat equation, space of convolutions, Lebesgue point
Keywords: Hölder's inequality. 
@article{MZM_2018_103_6_a0,
     author = {D. N. Bushev and Yu. I. Kharkevich},
     title = {Finding {Solution} {Subspaces} of the {Laplace} and {Heat} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {803--817},
     publisher = {mathdoc},
     volume = {103},
     number = {6},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_6_a0/}
}
TY  - JOUR
AU  - D. N. Bushev
AU  - Yu. I. Kharkevich
TI  - Finding Solution Subspaces of the Laplace and Heat Equations
JO  - Matematičeskie zametki
PY  - 2018
SP  - 803
EP  - 817
VL  - 103
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2018_103_6_a0/
LA  - ru
ID  - MZM_2018_103_6_a0
ER  - 
%0 Journal Article
%A D. N. Bushev
%A Yu. I. Kharkevich
%T Finding Solution Subspaces of the Laplace and Heat Equations
%J Matematičeskie zametki
%D 2018
%P 803-817
%V 103
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2018_103_6_a0/
%G ru
%F MZM_2018_103_6_a0
D. N. Bushev; Yu. I. Kharkevich. Finding Solution Subspaces of the Laplace and Heat Equations. Matematičeskie zametki, Tome 103 (2018) no. 6, pp. 803-817. http://geodesic.mathdoc.fr/item/MZM_2018_103_6_a0/