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Constructing an elementary measure on a space of projections
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UNSPECIFIED (2002) Constructing an elementary measure on a space of projections. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 267 (2). pp. 714-725. doi:10.1006/jmaa.2001.7809 ISSN 0022-247X.
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Official URL: http://dx.doi.org/10.1006/jmaa.2001.7809
Abstract
Bypassing much theory from integral geometry, we construct an elementary measure on a space whose elements can represent rank k orthogonal projections in R-N. By replacing the Grassmannian G(N,k) with a simple product space circle times(j=1)(k) SN-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. (C) 2002 Elsevier Science (USA).
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | ||||
Publisher: | ACADEMIC PRESS INC ELSEVIER SCIENCE | ||||
ISSN: | 0022-247X | ||||
Official Date: | 15 March 2002 | ||||
Dates: |
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Volume: | 267 | ||||
Number: | 2 | ||||
Number of Pages: | 12 | ||||
Page Range: | pp. 714-725 | ||||
DOI: | 10.1006/jmaa.2001.7809 | ||||
Publication Status: | Published |
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