scholarly journals RETRACTED ARTICLE: A note on the boundary behavior for a modified Green function in the upper-half space

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Yulian Zhang ◽  
Valery Piskarev
Keyword(s):  
Green Function ◽  
Euclidean Space ◽  
Half Space ◽  
Boundary Behavior ◽  
Indian Acad ◽  
Boundary Property ◽  
Dimensional Euclidean Space ◽  
Retracted Article ◽  
Green Potential

Abstract Motivated by (Xu et al. in Bound. Value Probl. 2013:262, 2013) and (Yang and Ren in Proc. Indian Acad. Sci. Math. Sci. 124(2):175-178, 2014), in this paper we aim to construct a modified Green function in the upper-half space of the n-dimensional Euclidean space, which generalizes the boundary property of general Green potential.

scholarly journals Modified Poisson Integral and Green Potential on a Half-Space

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Lei Qiao
Keyword(s):  
Euclidean Space ◽  
Half Space ◽  
Analytic Functions ◽  
Harmonic Functions ◽  
Poisson Integral ◽  
Dimensional Euclidean Space ◽  
Superharmonic Functions ◽  
Growth Properties ◽  
Green Potential

We discuss the behavior at infinity of modified Poisson integral and Green potential on a half-space of then-dimensional Euclidean space, which generalizes the growth properties of analytic functions, harmonic functions and superharmonic functions.

scholarly journals The number of partitions of a set of N points in k dimensions induced by hyperplanes

1967 ◽  
Vol 15 (4) ◽  
pp. 285-289 ◽  
Author(s):  
E. F. Harding
Keyword(s):  
Euclidean Space ◽  
Half Space ◽  
General Position ◽  
The Other ◽  
Dimensional Euclidean Space ◽  
Unordered Pair

1. An arbitrary (k– 1)-dimensional hyperplane disconnects K-dimensional Euclidean space Ek into two disjoint half-spaces. If a set of N points in general position in Ek is given [nok +1 in a (k–1)-plane, no k in a (k–2)-plane, and so on], then the set is partitione into two subsets by the hyperplane, a point belonging to one or the other subset according to which half-space it belongs to; for this purpose the half-spaces are considered as an unordered pair.

A Comparison Between thin Sets and Generalized Azarin Sets

1975 ◽  
Vol 18 (3) ◽  
pp. 335-346 ◽  
Author(s):  
M. Essén ◽  
H. L. Jackson
Keyword(s):  
Euclidean Space ◽  
Half Space ◽  
Martin Boundary ◽  
Dimensional Euclidean Space ◽  
Thin Sets

Let Rp(p≥2) denote p-dimensional Euclidean space, D the half space defined by {P = (x1, x2, …, xp) ∊ Rp: xp > 0} and ∂D the frontier of D in Rp. The Martin boundary (see [2]) of D can be identified with ∂D∪{∞}.

scholarly journals Boundary behavior of positive harmonic functions in balls of Rn

1981 ◽  
Vol 84 ◽  
pp. 1-8
Author(s):  
Michael Von Renteln
Keyword(s):  
Euclidean Space ◽  
Harmonic Functions ◽  
Boundary Behavior ◽  
Euclidean Norm ◽  
Dimensional Euclidean Space ◽  
Open Ball ◽  
The Real ◽  
Positive Harmonic Functions

Let Rn be the real n-dimensional euclidean space. Elements of Rn are denoted by x = (xl • • •, xn), and ‖ x ‖ denotes the euclidean norm of x.The open ball B(x, r) with center x and radius r is defined by

scholarly journals Retraction Note: A note on the boundary behavior for a modified Green function in the upper-half space

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yulian Zhang ◽  
Valery Piskarev
Keyword(s):  
Green Function ◽  
Half Space ◽  
Boundary Behavior ◽  
Link Type ◽  
Retraction Notice

This article has been retracted. Please see the retraction notice for more detail: 10.1186/s13661-015-0363-z.

scholarly journals Growth properties of modified α-potentials in the upper-half space

Filomat ◽  
2013 ◽  
Vol 27 (4) ◽  
pp. 703-712 ◽  
Author(s):  
Lei Qiao ◽  
Guantie Deng
Keyword(s):  
Euclidean Space ◽  
Half Space ◽  
Analytic Functions ◽  
Harmonic Functions ◽  
Dimensional Euclidean Space ◽  
Superharmonic Functions ◽  
Growth Properties ◽  
Modified Kernels

The aim of this paper is to discuss the behavior at infinity of modified ?-potentials represented by the modified kernels in the upper-half space of the n-dimensional Euclidean space, which generalizes the growth properties of analytic functions, harmonic functions and superharmonic functions.

On Vitali's Theorem for Groups of Motions of Euclidean Space

1999 ◽  
Vol 6 (4) ◽  
pp. 323-334
Author(s):  
A. Kharazishvili
Keyword(s):  
Euclidean Space ◽  
Dimensional Euclidean Space ◽  
Finite Dimensional

Abstract We give a characterization of all those groups of isometric transformations of a finite-dimensional Euclidean space, for which an analogue of the classical Vitali theorem [Sul problema della misura dei gruppi di punti di una retta, 1905] holds true. This characterization is formulated in purely geometrical terms.

Some properties of Wigner coefficients and hyperspherical harmonics

1956 ◽  
Vol 52 (3) ◽  
pp. 424-430 ◽  
Author(s):  
A. P. Stone
Keyword(s):  
Angular Momentum ◽  
Euclidean Space ◽  
Rotation Group ◽  
Dimensional Euclidean Space ◽  
Hyperspherical Harmonics ◽  
Shift Operators ◽  
Analytical Relations

ABSTRACTGeneral shift operators for angular momentum are obtained and applied to find closed expressions for some Wigner coefficients occurring in a transformation between two equivalent representations of the four-dimensional rotation group. The transformation gives rise to analytical relations between hyperspherical harmonics in a four-dimensional Euclidean space.

On inequalities of the Tchebychev type

1963 ◽  
Vol 59 (1) ◽  
pp. 135-146 ◽  
Author(s):  
J. F. C. Kingman
Keyword(s):  
Probability Theory ◽  
Euclidean Space ◽  
Random Variable ◽  
Dimensional Euclidean Space ◽  
Real Random Variable ◽  
Finite Dimensional

1. A type of problem which frequently occurs in probability theory and statistics can be formulated in the following way. We are given real-valued functions f(x), gi(x) (i = 1, 2, …, k) on a space (typically finite-dimensional Euclidean space). Then the problem is to set bounds for Ef(X), where X is a random variable taking values in , about which all we know is the values of Egi(X). For example, we might wish to set bounds for P(X > a), where X is a real random variable with some of its moments given.

Sign in / Sign up

Export Citation Format

Share Document