...lopedia/old_files/data/B017/B.0107390 Boundary value problems in potential theory
...sses. It follows, therefore, that the boundary value problems of potential theory are primarily boundary value problems for elliptic equations and systems (c
5 KB (673 words) - 06:29, 30 May 2020
...erharmonic function on $X$ or, which amounts to the same thing, a positive potential, $X$ is known as a Green space. Thus, the Euclidean space $\mathbf R^n$, it
...matic potential theory (cf. [[Potential theory, abstract|Potential theory, abstract]]).
2 KB (357 words) - 11:31, 27 October 2014
For potential authors:
[[Abstract prime number theory]] |
1 KB (118 words) - 17:47, 25 April 2012
...nic space|Harmonic space]]; [[Potential theory, abstract|Potential theory, abstract]].)
...References|[a3]]]. Later on, more general axiomatic settings for potential theory were developed, mainly by H. Bauer, C. Constantinescu and A. Cornea, J. Bli
5 KB (700 words) - 18:48, 26 February 2024
is the [[Newton potential|Newton potential]] with density $ t $
...]</TD> <TD valign="top"> N.S. Landkof, "Foundations of modern potential theory" , Springer (1972) (Translated from Russian)</TD></TR></table>
4 KB (696 words) - 08:25, 6 June 2020
...potential theory (see also [[Potential theory, abstract|Potential theory, abstract]]), see [[#References|[a1]]], where it is called the axiom of natural decom
...>[a1]</td> <td valign="top"> C. Constantinescu, A. Cornea, "Potential theory on harmonic spaces" , Springer (1972) pp. 104</td></tr><tr><td valign="to
3 KB (449 words) - 17:00, 1 July 2020
...matic potential theory (cf. [[Potential theory, abstract|Potential theory, abstract]]) the equality of the best and the least harmonic majorant is connected to
...>[a1]</TD> <TD valign="top"> C. Constantinescu, A. Cornea, "Potential theory on harmonic spaces" , Springer (1972)</TD></TR></table>
3 KB (464 words) - 19:43, 5 June 2020
...encyclopediaofmath.org/legacyimages/b/b015/b015110/b01511017.png" /> whose
potential <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/l
...ediaofmath.org/legacyimages/b/b015/b015110/b01511040.png" /> in which each
potential <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/l
21 KB (2,931 words) - 16:56, 7 February 2011
Balayaged functions were introduced in classical [[Potential theory|potential theory]] by M. Brelot and play an important role. Given any set $A \subset \mathbf
...af|sheaf]] $\mathcal{H}$ of "harmonic" functions. Main model examples of abstract harmonic spaces are described by solutions of the [[Laplace equation|Laplac
6 KB (870 words) - 16:57, 1 July 2020
...of this axiomatic approach consists in the fact that if it is adopted, the theory comprises not only solutions of the [[Laplace equation|Laplace equation]],
...ch any positive harmonic minorant is identically equal to zero is called a potential. A harmonic space $ X $
7 KB (1,087 words) - 19:43, 5 June 2020
==Theory of games==
A relation expressing the superiority of one object ([[strategy (in game theory)]]; [[sharing]]) over another. Domination of strategies: A strategy $ s $
7 KB (1,044 words) - 19:36, 5 June 2020
A set function arising in [[Potential theory|potential theory]] as the analogue of the physical concept of the electrostatic capacity.
...ilibrium, potential of this compact set (cf. [[Capacity potential|Capacity potential]]), that is, the function harmonic everywhere outside $ K $,
17 KB (2,487 words) - 06:29, 30 May 2020
.../encyclopedia/old_files/data/K110/K.1100140 Korovkin\AAhtype approximation theory
...om Korovkin's theorems (cf. [[Korovkin theorems|Korovkin theorems]]), this theory consists of a collection of results whose main objective is to investigate
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...eaking, this asserts that a super- or subharmonic function is the sum of a potential and a harmonic function. For precise statements, see [[Subharmonic function
...e which has a subharmonic minorant may be written uniquely as the sum of a potential and a harmonic function. This harmonic function is the greatest hypo-harmon
8 KB (1,180 words) - 17:00, 1 July 2020
...for their relation with several aspects of convexity theory and potential theory.
...ems in the approximation of continuous functions by positive operators and abstract degenerate elliptic-parabolic problems have been discovered (see, e.g., [[#
2 KB (241 words) - 12:50, 4 September 2014
$#C+1 = 421 : ~/encyclopedia/old_files/data/P074/P.0704140 Potential theory
...(1828) a potential function and by C.F. Gauss (1840) — just a [[Potential|potential]]. At present, the achievements of this initial period are included in cour
38 KB (5,597 words) - 10:29, 30 January 2022
...zability|abstraction of potential realizability]] — leads to the idea of a potential infinity. This abstraction, in conjunction with the refusal to use the abst
...eory essentially depends on the nature of the fundamental concepts of this theory, and hence on the nature of the mathematical abstractions accepted in the f
4 KB (591 words) - 17:01, 7 February 2011
...]</TD> <TD valign="top"> N.S. Landkof, "Foundations of modern potential theory" , Springer (1972) (Translated from Russian)</TD></TR><TR><TD valign="top
..., [[#References|[a1]]] for irregular boundary points in abstract potential theory.
5 KB (799 words) - 09:19, 6 January 2024
as the sum of a [[Potential|potential]] and a [[Harmonic function|harmonic function]] $ h $
In abstract potential theory, a [[Potential|potential]] on an open set $ U $
6 KB (965 words) - 08:11, 6 June 2020
$#C+1 = 311 : ~/encyclopedia/old_files/data/P074/P.0704150 Potential theory, abstract
...see [[#References|[3]]]). The probabilistic approach to abstract potential theory, the origins of which could be found already in the works of P. Lévy, J. D
23 KB (3,517 words) - 08:07, 6 June 2020