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Do projections stay close together?

Abstract:

We estimate the rate of convergence of products of projections on K intersecting lines in Rd. More generally, consider the orbit of a point under any sequence of orthogonal projections on K arbitrary lines in Rd. Assume that the sum of the squares of the distances of the consecutive iterates is less than ε. We show that if ε tends to zero, then the diameter of the orbit tends to zero uniformly for all families L of a fixed number K of lines. We relate this result to questions concerning conve...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1016/j.jmaa.2008.09.039

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
Elsevier Publisher's website
Journal:
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS Journal website
Volume:
350
Issue:
2
Pages:
859-871
Publication date:
2009-02-15
DOI:
EISSN:
1096-0813
ISSN:
0022-247X
Source identifiers:
26491
Language:
English
Keywords:
UUID:
uuid:64281e6f-05d7-46c6-b69b-52a5303ff1c7
Local pid:
pubs:26491
Deposit date:
2012-12-19

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