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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A construction of Hilbert spaces of analytic functions


Author: William W. Hastings
Journal: Proc. Amer. Math. Soc. 74 (1979), 295-298
MSC: Primary 46E20; Secondary 47B20
MathSciNet review: 524303
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Abstract: A simple technique is presented for constructing a measure $ \nu$ from a given measure so that $ {R^2}(K,\nu )$ has certain properties. Here, $ {R^2}(K,\nu )$ is the closure in $ {L^2}(\nu )$ of the rational functions with poles off K, a compact set containing the support of $ \nu$. A typical example shows that there exists a measure $ \nu$ mutually absolutely continuous with area measure on the unit disk such that $ \sqrt z $ (principal branch) is an element of $ {R^2}(K,\nu )$, while each point of the open disk except on the negative real axis is an analytic bounded point evaluation for $ {R^2}(K,\nu )$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0524303-4
PII: S 0002-9939(1979)0524303-4
Article copyright: © Copyright 1979 American Mathematical Society