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Title: Partial sum process of orthogonal series as rough process
Author: Yang, Danyu
ISNI:       0000 0004 2745 9831
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2012
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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.
Supervisor: Lyons, Terry Sponsor: Clarendon Fund
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Functional analysis (mathematics) ; partial sum process ; orthogonal series ; rough path theory ; harmonic analysis