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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A note on a basis problem


Author: J. M. Anderson
Journal: Proc. Amer. Math. Soc. 51 (1975), 330-334
MSC: Primary 30A18
DOI: https://doi.org/10.1090/S0002-9939-1975-0379809-4
MathSciNet review: 0379809
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Abstract: It is shown that the functions $ \{ \exp - {\lambda _\nu }x\} _{\nu = 1}^\infty $ form a basis for the subspace of $ {\mathcal{L}_2}(0,\infty )$ which they span if and only if

$\displaystyle \mathop {\inf }\limits_\mu \prod\limits_{\nu = 1;\nu \ne \mu }^\i... ...ambda _\mu }}}{{{{\bar \lambda }_\nu } + {\lambda _\mu }}}\vert = \delta > 0.} $

The proof uses certain estimates concerning interpolation in $ {H_2}$ due to Shapiro and Shields. The proof makes explicit a construction embedded in a paper of Binmore [1, Theorems 9-12.].

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DOI: https://doi.org/10.1090/S0002-9939-1975-0379809-4
Keywords: Linear manifold, basis, interpolation
Article copyright: © Copyright 1975 American Mathematical Society