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Constructing an Elementary Measure on a Space of Projections

✍ Scribed by Peter K Friz; James C Robinson

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 108 KB
Volume: 267
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.2001.7809

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✦ Synopsis

Bypassing much theory from integral geometry, we construct an elementary measure on a space whose elements can represent rank k orthogonal projections in N . By replacing the Grassmannian G N k with a simple product space k j=1 S N-1 we are able to reproduce certain important features of the nontrivial measure on G N k invariant under the action of the orthogonal group (a property also enjoyed by our construction). As a motivating example we show that our construction enables the proof of a recent embedding theorem due to Foias and Olson to be completed using only standard methods of analysis.  2002 Elsevier Science (USA)

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