Sweeping at the Martin Boundary of a Fine Domain

被引：2

作者：

El Kadiri, Mohamed ^{[1
]}

Fuglede, Bent ^{[2
]}

机构：

[1] Univ Mohammed 5, Fac Sci, Dept Math, BP 1014, Rabat, Morocco

[2] Dept Math Sci, Univ Pk 5, DK-2100 Copenhagen, Denmark

来源：

POTENTIAL ANALYSIS | 2016年 / 44卷 / 02期

关键词：

Martin boundary; Riesz-Martin kernel; Finely superharmonic function; Finely harmonic function; Sweeping; Minimal thinness; Minimal-fine topology; INTEGRAL-REPRESENTATION; RIESZ-DECOMPOSITION;

D O I：

10.1007/s11118-015-9518-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study sweeping on a subset of the Riesz-Martin space of a fine domain in (na parts per thousand yen2), both with respect to the natural topology and the minimal-fine topology, and show that the two notions of sweeping are identical.

引用

页码：401 / 422

页数：22

共 50 条

[31] A Note on the Harnack Inequality Related with the Martin Boundary [J].

Ruan, H. -J. ;

Wang, X. -Y. .

MARKOV PROCESSES AND RELATED FIELDS, 2015, 21 (02) :283-292

[32] Martin boundary and exit space on the Sierpinski gasket [J].

LAU KaSing ;

NGAI SzeMan .

ScienceChina(Mathematics), 2012, 55 (03) :475-494

[33] Reflected random walks and unstable Martin boundary [J].

Ignatiouk-Robert, Irina ;

Kurkova, Irina ;

Raschel, Kilian .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2024, 60 (01) :549-587

[34] Invariant measure, ratio limits and martin boundary [J].

Zhao M. ;

Jin M. .

Applied Mathematics-A Journal of Chinese Universities, 2002, 17 (4) :465-472

[35] The Martin Boundary of the Young-Fibonacci Lattice [J].

Frederick M. Goodman ;

Sergei V. Kerov .

Journal of Algebraic Combinatorics, 2000, 11 :17-48

[36] Martin boundary and exit space on the Sierpinski gasket [J].

Ka-Sing Lau ;

Sze-Man Ngai .

Science China Mathematics, 2012, 55 :475-494

[37] MARTIN BOUNDARY OF A KILLED RANDOM WALK ON A QUADRANT [J].

Ignatiouk-Robert, Irina ;

Loree, Christophe .

ANNALS OF PROBABILITY, 2010, 38 (03) :1106-1142

[38] Potential Analysis on Nonsmooth Domains-Martin Boundary and Boundary Harnack Principle [J].

Aikawa, Hiroaki .

COMPLEX ANALYSIS AND POTENTIAL THEORY, 2012, 55 :235-253

[39] POST-CRITICALLY FINITE FRACTAL AND MARTIN BOUNDARY [J].

Ju, Hongbing ;

Lau, Ka-Sing ;

Wang, Xiang-Yang .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 364 (01) :103-118

[40] Martin Boundary of Killed Random Walks on Isoradial Graphs [J].

Cédric Boutillier ;

Kilian Raschel .

Potential Analysis, 2022, 57 :201-226

← 1 2 3 4 5 →