Sierpiński Gasket as a Martin Boundary I: Martin Kernels

Manfred Denker; Hiroshi Sato

doi:10.1023/A:1011232724842

Sierpiński Gasket as a Martin Boundary I: Martin Kernels

Manfred Denker, Hiroshi Sato

Mathematics

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26 Scopus citations

Abstract

We show that a Sierpiński gasket in N dimension is homeomorphic to the minimal Martin boundary of some canonical Markov chain. This provides a new class of examples for the boundary theory of Markov chains and the basis for a harmonic analysis on p.c.f. fractal structures.

Original language	English (US)
Pages (from-to)	211-232
Number of pages	22
Journal	Potential Analysis
Volume	14
Issue number	3
DOIs	https://doi.org/10.1023/A:1011232724842
State	Published - 2001

All Science Journal Classification (ASJC) codes

Analysis

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10.1023/A:1011232724842

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title = "Sierpi{\'n}ski Gasket as a Martin Boundary I: Martin Kernels",

abstract = "We show that a Sierpi{\'n}ski gasket in N dimension is homeomorphic to the minimal Martin boundary of some canonical Markov chain. This provides a new class of examples for the boundary theory of Markov chains and the basis for a harmonic analysis on p.c.f. fractal structures.",

author = "Manfred Denker and Hiroshi Sato",

note = "Funding Information: ∗ This research was supported by the Japan Society for Promotion of Science and the Deutsche Forschungsgemeinschaft.",

year = "2001",

doi = "10.1023/A:1011232724842",

language = "English (US)",

volume = "14",

pages = "211--232",

journal = "Potential Analysis",

issn = "0926-2601",

publisher = "Springer Netherlands",

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T1 - Sierpiński Gasket as a Martin Boundary I

T2 - Martin Kernels

AU - Denker, Manfred

AU - Sato, Hiroshi

N1 - Funding Information: ∗ This research was supported by the Japan Society for Promotion of Science and the Deutsche Forschungsgemeinschaft.

PY - 2001

Y1 - 2001

N2 - We show that a Sierpiński gasket in N dimension is homeomorphic to the minimal Martin boundary of some canonical Markov chain. This provides a new class of examples for the boundary theory of Markov chains and the basis for a harmonic analysis on p.c.f. fractal structures.

AB - We show that a Sierpiński gasket in N dimension is homeomorphic to the minimal Martin boundary of some canonical Markov chain. This provides a new class of examples for the boundary theory of Markov chains and the basis for a harmonic analysis on p.c.f. fractal structures.

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U2 - 10.1023/A:1011232724842

DO - 10.1023/A:1011232724842

M3 - Article

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EP - 232

JO - Potential Analysis

JF - Potential Analysis

IS - 3

ER -

Sierpiński Gasket as a Martin Boundary I: Martin Kernels

Abstract

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