<oai_dc:dc xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
<dc:title>Energy measures of harmonic functions on the Sierpinski gasket</dc:title>
<dc:creator>Renee Bell</dc:creator><dc:creator>Ching wei Ho</dc:creator><dc:creator>Robert Strichartz</dc:creator>
<dc:subject>28A80</dc:subject><dc:subject>Sierpinski gasket</dc:subject><dc:subject>energy measures</dc:subject><dc:subject>Kusuoka measure</dc:subject><dc:subject>energy Laplacian</dc:subject><dc:subject>Radon-Nikodym derivatives</dc:subject>
<dc:description>We study energy measures on SG based on harmonic functions. We characterize the positive energy measures through studying the bounds of Radon-Nikodym derivatives with respect to the Kusuoka measure. We prove a limited continuity of the derivative on the graph $V_{*}$, and express the average value of the derivative on a whole cell as a weighted average of the values on the boundary vertices. We also prove some characterizations and properties of the weights.</dc:description>
<dc:publisher>Indiana University Mathematics Journal</dc:publisher>
<dc:date>2014</dc:date>
<dc:type>text</dc:type>
<dc:format>pdf</dc:format>
<dc:identifier>10.1512/iumj.2014.63.5256</dc:identifier>
<dc:source>10.1512/iumj.2014.63.5256</dc:source>
<dc:language>en</dc:language>
<dc:relation>Indiana Univ. Math. J. 63 (2014) 831 - 868</dc:relation>
<dc:coverage>state-of-the-art mathematics</dc:coverage>
<dc:rights>http://iumj.org/access/</dc:rights>
</oai_dc:dc>