In this thesis, we investigate the pathwise regularity of partial sum process of general orthogonal series, and prove that the partial sum process is a geometric 2-rough process under the same condition as in Menshov-Rademacher Theorem. For Fourier series, the condition can be improved, and an equivalent condition on the limit function is identified.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:581175 |
| Date | January 2012 |
| Creators | Yang, Danyu |
| Contributors | Lyons, Terry |
| Publisher | University of Oxford |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://ora.ox.ac.uk/objects/uuid:f48d69b9-29ba-420b-a6b5-55deba847b15 |
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