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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Uniform analyticity of orthogonal projections


Authors: R. R. Coifman and Margaret A. M. Murray
Journal: Trans. Amer. Math. Soc. 312 (1989), 779-817
MSC: Primary 42A05; Secondary 33A65, 42C10, 46N05, 47B38, 58F07
DOI: https://doi.org/10.1090/S0002-9947-1989-0951882-6
MathSciNet review: 951882
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Abstract: Let $ X$ denote the circle $ T$ or the interval $ [ - 1,1]$, and let $ d\mu $ denote a nonnegative, absolutely continuous measure on $ X$ . Under what conditions does the Gram-Schmidt procedure in the weighted space $ {L^2}(X,{\omega ^2}\;d\mu)$ depend analytically on the logarithm of the weight function $ \omega $? In this paper, we show that, in numerous examples of interest, $ \log \omega \in BMO$ is a sufficient (often necessary!) condition for analyticity of the Gram-Schmidt procedure. These results are then applied to establish the local analyticity of certain infinite-dimensional Toda flows.


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DOI: https://doi.org/10.1090/S0002-9947-1989-0951882-6
Article copyright: © Copyright 1989 American Mathematical Society