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arXiv · 1306.2231

"Graph Paper" Trace Characterizations of Functions of Finite Energy

Robert S. Strichartz
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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 $mn$ for all $n$, and certain $\12-$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.

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Robert S. Strichartz. 2013-06-10. "Graph Paper" Trace Characterizations of Functions of Finite Energy. https://arxiv.org/abs/1306.2231

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