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Weighted-$ L^2$ interpolation on non-uniformly separated sequences


Author: Stanislav Ostrovsky
Journal: Proc. Amer. Math. Soc. 138 (2010), 4413-4422
MSC (2000): Primary 30H05, 30D15, 32A36
DOI: https://doi.org/10.1090/S0002-9939-2010-10193-4
Published electronically: June 15, 2010
MathSciNet review: 2680065
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Abstract: We define a weighted-$ \ell^2$-norm associated to a discrete sequence $ \Gamma$ in $ \mathbb{C}$ and a weight function $ \varphi$. We then give a sufficient condition which ensures that we can always extend weighted-$ \ell^2$ data to global holomorphic functions which are also weighted-$ L^2$. The condition is such that the so-called upper density of $ \Gamma$ is strictly less than one.


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Additional Information

Stanislav Ostrovsky
Affiliation: Department of Mathematics, Stony Brook University, Stony Brook, New York 11794-3651
Email: stas@math.sunsysb.edu

DOI: https://doi.org/10.1090/S0002-9939-2010-10193-4
Keywords: Interpolation, $L^{2}$-methods, Beurling density
Received by editor(s): February 10, 2009
Published electronically: June 15, 2010
Communicated by: Mario Bonk
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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