"Graph Paper" Trace Characterizations of Functions of Finite Energy
Functional Analysis
2016-11-26 v1
Abstract
We characterize functions of finite energy in the plane in terms of their traces on the lines that make up "graph paper" with squares of side length for all , and certain order Sobolev norms on the graph paper lines. We also obtain analogous results for functions of finite energy on two classical fractals: the Sierpinski gasket and the Sierpinski carpet.
Keywords
Cite
@article{arxiv.1306.2231,
title = {"Graph Paper" Trace Characterizations of Functions of Finite Energy},
author = {Robert S. Strichartz},
journal= {arXiv preprint arXiv:1306.2231},
year = {2016}
}