Reflections on harmonic analysis of the Sierpinski gasket

被引：0
|
作者：
Denker, M
Sato, H
机构：
[1] Univ Gottingen, Inst Math Stochastik, D-37083 Gottingen, Germany
[2] Kyushu Univ, Grad Sch Math, Fukuoka 8128581, Japan
来源：
MATHEMATISCHE NACHRICHTEN | 2002年 / 241卷
关键词：
Sierpinski gasket; harmonic function; Laplace operator; Martin boundary;
D O I：
10.1002/1522-2616(200207)241:1<32::AID-MANA32>3.0.CO;2-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Based on the geometric structure of the Sierpinski gasket, KIGAMI [10], [11] established the harmonic analysis for the gasket analytically. On the other hand DENKER and SATO [3] proved that the Sierpinski gasket S in R-N has a natural description as the Martin boundary for some canonical Markov chain on the word space. The aim of this paper is to reveal the connection between the harmonic analysis of the Markov chain and that of the Sierpinski gasket viewed as a Martin boundary, and to describe this analysis in terms of the Markov operator, the Martin kernel and the structure of the word space.
引用
收藏
页码：32 / 55
页数：24
相关论文
共 50 条
  • [41] Hausdorff measure of Sierpinski gasket
    周作领
    Science China Mathematics, 1997, (10) : 1016 - 1021
  • [42] Eikonal equations on the Sierpinski gasket
    Camilli, Fabio
    Capitanelli, Raffaela
    Marchi, Claudio
    MATHEMATISCHE ANNALEN, 2016, 364 (3-4) : 1167 - 1188
  • [43] Spanning trees on the Sierpinski gasket
    Chang, Shu-Chiuan
    Chen, Lung-Chi
    Yang, Wei-Shih
    JOURNAL OF STATISTICAL PHYSICS, 2007, 126 (03) : 649 - 667
  • [44] Broadcasting in Sierpinski gasket graphs
    Shanthakumari, A.
    Journal of Combinatorial Mathematics and Combinatorial Computing, 2015, 92 : 111 - 119
  • [45] MAGNETOINDUCTANCE OF A SUPERCONDUCTING SIERPINSKI GASKET
    KORSHUNOV, SE
    MEYER, R
    MARTINOLI, P
    PHYSICAL REVIEW B, 1995, 51 (09): : 5914 - 5926
  • [46] Orthogonal Polynomials on the Sierpinski Gasket
    Kasso A. Okoudjou
    Robert S. Strichartz
    Elizabeth K. Tuley
    Constructive Approximation, 2013, 37 : 311 - 340
  • [47] Magnetoinductance of a superconducting Sierpinski gasket
    Korshunov, S. E.
    Meyer, R.
    Martinoli, P.
    Physical Review B: Condensed Matter, 51 (09):
  • [48] Orthogonal Polynomials on the Sierpinski Gasket
    Okoudjou, Kasso A.
    Strichartz, Robert S.
    Tuley, Elizabeth K.
    CONSTRUCTIVE APPROXIMATION, 2013, 37 (03) : 311 - 340
  • [49] Spanning forests on the Sierpinski gasket
    Department of Physics, National Cheng Kung University, Tainan 70101, Taiwan
    不详
    Discrete Mathematics and Theoretical Computer Science, 2008, 10 (02): : 55 - 76
  • [50] Fractal functions on the Sierpinski Gasket
    Ri, SongIl
    CHAOS SOLITONS & FRACTALS, 2020, 138
12345