Date of Award
2016
Document Type
Dissertation
Publication Status
Version of Record
Submission Date
October 2026
Thesis/Dissertation Advisor [Chair]
Sagher, Yoram
Abstract
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.
Extent
57 p.
Recommended Citation
Rutherfoord, Vermont Charles, "Negligible Variation, Change of Variables, and a Smooth Analog of the Hobby-Rice Theorem" (2016). Electronic Theses and Dissertations 2010 - 2019. 1519.
https://digitalcommons.fau.edu/etd_general_6/1519
Identifier
FA00004627
Comments
Includes bibliography.|Dissertation (Ph.D.)--Florida Atlantic University, 2016.|FAU Electronic Theses and Dissertations Collection|Includes bibliography.