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Analysis On Infinite Trees and Their Boundaries

Title:

Analysis On Infinite Trees and Their Boundaries

Pevzner, Chana (2018) Analysis On Infinite Trees and Their Boundaries. Masters thesis, Concordia University.

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Abstract

The aim of this thesis is to understand the results of Björn, Björn, Gill and Shanmugalingam [BBGS], who give an analogue of the famous Trace Theorem for Sobolev spaces on the infinite K-ary tree and its boundary. In order to do so, we investigate the properties of a tree as a metric measure space, namely the doubling condition and Poincaré inequality, and study the boundary in terms of geodesic rays as well as random walks. We review the definitions of the appropriate Sobolev and Besov spaces and the proof of the Trace Theorem in [BBGS].

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Pevzner, Chana
Institution:Concordia University
Degree Name:M. Sc.
Program:Mathematics
Date:30 July 2018
Thesis Supervisor(s):Dafni, Galia
ID Code:984360
Deposited By: CHANA PEVZNER
Deposited On:12 Nov 2018 18:07
Last Modified:12 Nov 2018 18:07
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