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Two-norm spaces
Author
Leo, Chin Choon
Supervisor
Lee, Peng Yee
Abstract
In 1966, Hildebrandt proved the representation theorems for linear functionals defined on the space of bounded variation (BV) functions, regarding BV as a two-norm space. Hildebrandt's work was followed up by Kiang Kiang Aye and Lee Peng Yee and in 2002, they reformulated his results in terms of the Henstock-Stieltjes (HS) integral and established a duality between the space of BV and regulated functions (W).
In this thesis, we begin by regarding BV as a two-norm space, and make an eventual observation that a continuous linear functional F defined on BV can he represented by a sum involving a HS integral and a series. This is a result obtained originally by Kiang Kiang Aye, which is similar to Hildebrandt's version. The duality of BV and RF, however, will not be included here.
In this thesis, we begin by regarding BV as a two-norm space, and make an eventual observation that a continuous linear functional F defined on BV can he represented by a sum involving a HS integral and a series. This is a result obtained originally by Kiang Kiang Aye, which is similar to Hildebrandt's version. The duality of BV and RF, however, will not be included here.
Date Issued
2005
Call Number
QA323 Leo
Date Submitted
2005