This dissertation concerns two topics in analysis. The rst section is an exposition
of the Henstock-Kurzweil integral leading to a necessary and su cient condition
for the change of variables formula to hold, with implications for the change
of variables formula for the Lebesgue integral. As a corollary, a necessary and suf-
cient condition for the Fundamental Theorem of Calculus to hold for the HK integral
is obtained. The second section concerns a challenge raised in a paper by O.
Lazarev and E. H. Lieb, where they proved that, given f1….,fn ∈ L1 ([0,1] ; C),
there exists a smooth function φ that takes values on the unit circle and annihilates
span {f1...., fn}. We give an alternative proof of that fact that also shows the W1,1
norm of φ can be bounded by 5πn + 1. Answering a question raised by Lazarev and
Lieb, we show that if p > 1 then there is no bound for the W1,p norm of any such
multiplier in terms of the norms of f1...., fn. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2016. / FAU Electronic Theses and Dissertations Collection
| Identifer | oai:union.ndltd.org:fau.edu/oai:fau.digital.flvc.org:fau_33486 |
| Contributors | Rutherfoord, Vermont Charles (author), Sagher, Yoram (Thesis advisor), Florida Atlantic University (Degree grantor), Charles E. Schmidt College of Science, Department of Mathematical Sciences |
| Publisher | Florida Atlantic University |
| Source Sets | Florida Atlantic University |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation, Text |
| Format | 57 p., application/pdf |
| Rights | Copyright © is held by the author, with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder., http://rightsstatements.org/vocab/InC/1.0/ |
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