English

"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 mnmn for all nn, and certain \12\12-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}
}