Francos, Gregory Peter
(2011)
Luzin Type Approximation of Functions of Bounded Variation.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
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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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
| Creators | Email | Pitt Username | ORCID  |
|---|
| Francos, Gregory Peter | gpf3@pitt.edu | GPF3 | |
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| ETD Committee: |
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| 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: |
http://etd.library.pitt.edu/ETD/available/etd-05242011-140235/, etd-05242011-140235 |
| Date Deposited: |
10 Nov 2011 19:45 |
| Last Modified: |
15 Nov 2016 13:43 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/7947 |
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