Trace and Density Results on Regular Trees

Pekka Koskela, Khanh Ngoc Nguyen, Zhuang Wang

Type: Article

Publication Date: 2021-03-06

Citations: 5

DOI: https://doi.org/10.1007/s11118-021-09907-2

Abstract

Abstract The boundary of a regular tree can be viewed as a Cantor-type set. We equip our tree with a weighted distance and a weighted measure via the Euclidean arc-length and consider the associated first-order Sobolev spaces. We give characterizations for the existence of traces and for the density of compactly supported functions.

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arXiv (Cornell University) - View - PDF
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