Resistance Forms on Self-Similar Sets with Finite Ramification of Finite Type
In this paper, we introduce the finite neighboring type and the finite chain length conditions for a connected self-similar set K . We show that with these two conditions, K is a finitely ramified graph directed (f.r.g.d.) fractal defined by Hambly and Nyberg (Proc. Edinb. Math. Soc. (2) 46 (1), 1–3...
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| Veröffentlicht in: | Potential analysis 2021-04, Vol.54 (4), p.581-606 |
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| creator | Cao, Shiping Qiu, Hua |
| description | In this paper, we introduce the finite neighboring type and the finite chain length conditions for a connected self-similar set
K
. We show that with these two conditions,
K
is a finitely ramified graph directed (f.r.g.d.) fractal defined by Hambly and Nyberg (Proc. Edinb. Math. Soc. (2)
46
(1), 1–34
2003
). We give some nontrivial examples and compute the harmonic structures on them explicitly. Furthermore, for a f.r.g.d. self-similar set
K
, we provide an equivalent description, the finitely ramified of finite type (f.r.f.t.) cell structure of
K
, and investigate the relationship of harmonic structures associated with different f.r.f.t. cell structures of
K
. |
| doi_str_mv | 10.1007/s11118-020-09840-w |
| format | Article |
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K
. We show that with these two conditions,
K
is a finitely ramified graph directed (f.r.g.d.) fractal defined by Hambly and Nyberg (Proc. Edinb. Math. Soc. (2)
46
(1), 1–34
2003
). We give some nontrivial examples and compute the harmonic structures on them explicitly. Furthermore, for a f.r.g.d. self-similar set
K
, we provide an equivalent description, the finitely ramified of finite type (f.r.f.t.) cell structure of
K
, and investigate the relationship of harmonic structures associated with different f.r.f.t. cell structures of
K
.</description><identifier>ISSN: 0926-2601</identifier><identifier>EISSN: 1572-929X</identifier><identifier>DOI: 10.1007/s11118-020-09840-w</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Functional Analysis ; Geometry ; Mathematics ; Mathematics and Statistics ; Potential Theory ; Probability Theory and Stochastic Processes ; Self-similarity</subject><ispartof>Potential analysis, 2021-04, Vol.54 (4), p.581-606</ispartof><rights>Springer Nature B.V. 2020</rights><rights>Springer Nature B.V. 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-bb4ee2112bf060b829bdcd8414ff98134d7ff92e1c05b819661de3744050beb43</citedby><cites>FETCH-LOGICAL-c319t-bb4ee2112bf060b829bdcd8414ff98134d7ff92e1c05b819661de3744050beb43</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11118-020-09840-w$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11118-020-09840-w$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27922,27923,41486,42555,51317</link.rule.ids></links><search><creatorcontrib>Cao, Shiping</creatorcontrib><creatorcontrib>Qiu, Hua</creatorcontrib><title>Resistance Forms on Self-Similar Sets with Finite Ramification of Finite Type</title><title>Potential analysis</title><addtitle>Potential Anal</addtitle><description>In this paper, we introduce the finite neighboring type and the finite chain length conditions for a connected self-similar set
K
. We show that with these two conditions,
K
is a finitely ramified graph directed (f.r.g.d.) fractal defined by Hambly and Nyberg (Proc. Edinb. Math. Soc. (2)
46
(1), 1–34
2003
). We give some nontrivial examples and compute the harmonic structures on them explicitly. Furthermore, for a f.r.g.d. self-similar set
K
, we provide an equivalent description, the finitely ramified of finite type (f.r.f.t.) cell structure of
K
, and investigate the relationship of harmonic structures associated with different f.r.f.t. cell structures of
K
.</description><subject>Functional Analysis</subject><subject>Geometry</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Potential Theory</subject><subject>Probability Theory and Stochastic Processes</subject><subject>Self-similarity</subject><issn>0926-2601</issn><issn>1572-929X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLAzEUhYMoWKt_wNWA6-i9mcwjSylWhYrQVnAXJjOJpsyjJiml_97oKO68m_vgnHPhI-QS4RoBihuPsUoKDCiIkgPdH5EJZgWjgonXYzIBwXLKcsBTcub9BgBYUZQT8rTU3vpQ9bVO5oPrfDL0yUq3hq5sZ9vKxSX4ZG_DezK3vQ06WVadNbaugo3Swfye14etPicnpmq9vvjpU_Iyv1vPHuji-f5xdrugdYoiUKW41gyRKQM5qJIJ1dRNyZEbI0pMeVPEgWmsIVMlijzHRqcF55CB0oqnU3I15m7d8LHTPsjNsHN9fClZBshFhJJGFRtVtRu8d9rIrbNd5Q4SQX5hkyM2GbHJb2xyH03paPJR3L9p9xf9j-sTR_Zv1w</recordid><startdate>20210401</startdate><enddate>20210401</enddate><creator>Cao, Shiping</creator><creator>Qiu, Hua</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20210401</creationdate><title>Resistance Forms on Self-Similar Sets with Finite Ramification of Finite Type</title><author>Cao, Shiping ; Qiu, Hua</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-bb4ee2112bf060b829bdcd8414ff98134d7ff92e1c05b819661de3744050beb43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Functional Analysis</topic><topic>Geometry</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Potential Theory</topic><topic>Probability Theory and Stochastic Processes</topic><topic>Self-similarity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cao, Shiping</creatorcontrib><creatorcontrib>Qiu, Hua</creatorcontrib><collection>CrossRef</collection><jtitle>Potential analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Cao, Shiping</au><au>Qiu, Hua</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Resistance Forms on Self-Similar Sets with Finite Ramification of Finite Type</atitle><jtitle>Potential analysis</jtitle><stitle>Potential Anal</stitle><date>2021-04-01</date><risdate>2021</risdate><volume>54</volume><issue>4</issue><spage>581</spage><epage>606</epage><pages>581-606</pages><issn>0926-2601</issn><eissn>1572-929X</eissn><abstract>In this paper, we introduce the finite neighboring type and the finite chain length conditions for a connected self-similar set
K
. We show that with these two conditions,
K
is a finitely ramified graph directed (f.r.g.d.) fractal defined by Hambly and Nyberg (Proc. Edinb. Math. Soc. (2)
46
(1), 1–34
2003
). We give some nontrivial examples and compute the harmonic structures on them explicitly. Furthermore, for a f.r.g.d. self-similar set
K
, we provide an equivalent description, the finitely ramified of finite type (f.r.f.t.) cell structure of
K
, and investigate the relationship of harmonic structures associated with different f.r.f.t. cell structures of
K
.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s11118-020-09840-w</doi><tpages>26</tpages></addata></record> |
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| ispartof | Potential analysis, 2021-04, Vol.54 (4), p.581-606 |
| issn | 0926-2601 1572-929X |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Functional Analysis Geometry Mathematics Mathematics and Statistics Potential Theory Probability Theory and Stochastic Processes Self-similarity |
| title | Resistance Forms on Self-Similar Sets with Finite Ramification of Finite Type |
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