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Luzin Type Approximation of Functions of Bounded Variation

Francos, Gregory Peter (2011) Luzin Type Approximation of Functions of Bounded Variation. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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This paper is divided into two sections:(I) Consider the function space BV^m = {u ∈ W^{m-1,1}: D^α u is a measure for |α| = m}Such functions are called mth order functions of bounded variation. We show that a function in BV^m(R^n) possesses the so-called C^m-Luzin property; that is, it coincides with a C^m(R^n) function outside a set of arbitrarily small Lebesgue measure.(II) Consider a set of Lebesgue measureable functions f^α: R^N &rarr R indexed by themulti-indices in R^N of order |α| = m. We will prove that for any such collection, there isg &isin C^{m-1}(R^N) which is m-times differentiable almost everywhere, and such thatD^α g(x) = f^α(x) a.e. for all |α| = m.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Francos, Gregory Petergpf3@pitt.eduGPF3
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairHajlasz, Piotrhajlasz@pitt.eduHAJLASZ
Committee MemberBeatrous, Frankbeatrous@pitt.eduBEATROUS
Committee MemberLeoni,
Committee MemberManfredi, Juanmanfredi@pitt.eduMANFREDI
Date: 27 September 2011
Date Type: Completion
Defense Date: 6 May 2011
Approval Date: 27 September 2011
Submission Date: 24 May 2011
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Potential Theory; Distributions; Functions of Bounded Variation; Whitney Extension Theorem; Luzin Property; Real Analysis
Other ID:, etd-05242011-140235
Date Deposited: 10 Nov 2011 19:45
Last Modified: 15 Nov 2016 13:43


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