Complex Analysis on Planar Cell Complexes

This paper is an examination of the theory of discrete complex analysis that arises from the framework of a planar cell complex. Construction of this theory is largely integration-based. A combination of two cell complexes, the double and its associated diamond complex, allows for the development of a discrete Cauchy Integral Formula.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2008

Author dc:creator

• Arnold, Rachel Florence

Chair dc:contributor.committeechair

• Haskell, Peter E.

Committee members dc:contributor.committeemember

• Green, Edward L.
• Thomson, James E.

• Cell Decomposition
• Cauchy-Riemann Equation
• Discrete Differential Forms
• Hodge Decomposition
• Cauchy Integral Formula

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-05052008-134530

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/32230