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'Graph Paper' Trace Characterizations of Functions of Finite Energy
- Publication Year :
- 2013
- Publisher :
- arXiv, 2013.
-
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.
- Subjects :
- Discrete mathematics
Plane (geometry)
General Mathematics
010102 general mathematics
Voltage graph
Mathematics::General Topology
Graph paper
01 natural sciences
Sierpinski triangle
Functional Analysis (math.FA)
Mathematics - Functional Analysis
Sobolev space
Coxeter graph
Sierpinski carpet
0103 physical sciences
String graph
FOS: Mathematics
010307 mathematical physics
0101 mathematics
Analysis
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....3ae57fef05ec71e9c13363e85b2cfd8d
- Full Text :
- https://doi.org/10.48550/arxiv.1306.2231