Partial sum process of orthogonal series as rough process

<p>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...

Бүрэн тодорхойлолт

Номзүйн дэлгэрэнгүй
Үндсэн зохиолч: Yang, D
Бусад зохиолчид: Lyons, T
Формат: Дипломын ажил
Хэл сонгох:English
Хэвлэсэн: 2012
Нөхцлүүд:
Тодорхойлолт
Тойм:<p>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.</p>