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“Graph paper” trace characterizations of functions of finite energy

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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 m n for all n and certain 1/2-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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Authors and Affiliations

  1. Mathematics Department, Cornell University, Ithaca, NY, 14853, USA

    Robert S. Strichartz

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  1. Robert S. Strichartz
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Correspondence to Robert S. Strichartz.

Additional information

Research supported in part by the National Science Foundation, grant DMS-1162045.

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Strichartz, R.S. “Graph paper” trace characterizations of functions of finite energy. JAMA 128, 239–260 (2016). https://doi.org/10.1007/s11854-016-0008-x

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  • DOI: https://doi.org/10.1007/s11854-016-0008-x

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