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Extensions of BMO-functions and fixed points of contractive mappings in L2, I Shvartsman, Pavel 2013-04-24
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Title | Extensions of BMO-functions and fixed points of contractive mappings in L2, I |
Creator |
Shvartsman, Pavel |
Publisher | Banff International Research Station for Mathematical Innovation and Discovery |
Date Issued | 2013-04-24 |
Description | Let E be a closed subset of Rn of positive Lebesgue measure. We discuss a constructive algorithm which to every function f defined on E assigns its almostoptimalextensiontoafunctionF(f)∈BMO(Rn). Weobtaintheextension F(f) as a fixed point of a certain contractive mapping Tf : L2(Rn) → L2(Rn). The extension operator f → F(f) is non-linear, and in general it is not known whether there exists a continuous linear extension operator BMO(Rn)|E → BMO(Rn) for an arbitrary set E. In these talk we present a rather wide family of sets for which such extension op- erators exist. In particular, this family contains closures of domains with arbitrary internal and external cusps. The proof of this result is based on a solution to a similar problem for spaces of Lipschitz functions defined on subsets of a hyperbolic space. |
Extent | 54 minutes |
Subject |
Mathematics Functional analysis Real functions |
Type |
Moving Image |
FileFormat | video/mp4 |
Language | eng |
Notes | Author affiliation: Technion |
Series |
BIRS Workshop Lecture Videos (Banff, Alta) |
Date Available | 2014-08-06 |
Provider | Vancouver : University of British Columbia Library |
Rights | Attribution-NonCommercial-NoDerivs 2.5 Canada |
DOI | 10.14288/1.0056641 |
URI | http://hdl.handle.net/2429/49264 |
Affiliation |
Non UBC |
Peer Review Status | Unreviewed |
Scholarly Level | Faculty |
Rights URI | http://creativecommons.org/licenses/by-nc-nd/2.5/ca/ |
AggregatedSourceRepository | DSpace |
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https://iiif.library.ubc.ca/presentation/dsp.48630.1-0056641/manifest