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Tsougkas, Konstantinos
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Rocky Mountain Journal of Mathematics
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The Kusuoka measure and the energy Laplacian on level-k Sierpiński gasketsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2019 (English)In: Rocky Mountain Journal of Mathematics, ISSN 0035-7596, E-ISSN 1945-3795, Vol. 49, no 3, p. 945-961Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Project Euclid , 2019. Vol. 49, no 3, p. 945-961
##### Keywords [en]

energy Laplacian, Kusuoka measure, Laplacian pointwise formula, Sierpiński gasket
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:his:diva-23102DOI: 10.1216/rmj-2019-49-3-945ISI: 000482670400014Scopus ID: 2-s2.0-85071912629OAI: oai:DiVA.org:his-23102DiVA, id: diva2:1788087
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt609",{id:"formSmash:j_idt609",widgetVar:"widget_formSmash_j_idt609",multiple:true}); Available from: 2023-08-15 Created: 2023-08-15 Last updated: 2023-08-15Bibliographically approved
##### In thesis

We extend and survey results in the theory of analysis on fractal sets from the standard Laplacian on the Sierpinski gasket to the energy Laplacian, which is defined weakly by using the Kusuoka energy measure. We also extend results from the Sierpinski gasket to level-k Sierpinski gaskets, for all k ≤ 2. We observe that the pointwise formula for the energy Laplacian is valid for all level-k Sierpinski gaskets, SGk, and we provide a proof of a known formula for the renormalization constants of the Dirichlet form for postcritically finite self-similar sets along with a probabilistic interpretation of the Laplacian pointwise formula. We also provide a vector self-similar formula and a variable weight self-similar formula for the Kusuoka measure on SGk, as well as a formula for the scaling of the energy Laplacian. Copyright © 2019 Rocky Mountain Mathematics Consortium.

1. Combinatorial and analytical problems for fractals and their graph approximations$(function(){PrimeFaces.cw("OverlayPanel","overlay1788082",{id:"formSmash:j_idt960:0:j_idt970",widgetVar:"overlay1788082",target:"formSmash:j_idt960:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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