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Transactions of the American Mathematical Society

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

 

 

On approximation by shifts and a theorem of Wiener


Author: R. A. Zalik
Journal: Trans. Amer. Math. Soc. 243 (1978), 299-308
MSC: Primary 41A30
MathSciNet review: 0493077
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Abstract: We study the completeness in $ {L_2}(R)$ of sequences of the form $ \{ f({c_n} - t)\} $, where $ \{ {c_n}\} $ is a sequence of distinct real numbers. A Müntztype theorem is proved, valid for a large class of functions and, in particular, for $ f(t) = \exp ( - {t^2})$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0493077-1
Keywords: Approximation by sequences of shifts in $ {L_2}(R)$, entire functions of order 2, Fourier inversion
Article copyright: © Copyright 1978 American Mathematical Society