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Proceedings of the American Mathematical Society

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

 

 

Approximation by nonfundamental sequences of translates


Author: R. A. Zalik
Journal: Proc. Amer. Math. Soc. 78 (1980), 261-266
MSC: Primary 41A30
DOI: https://doi.org/10.1090/S0002-9939-1980-0550509-2
MathSciNet review: 550509
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Abstract: For functions $ f(t)$ satisfying certain growth conditions, we consider a sequence of the form $ \{ f({c_n} - t)\} $, nonfundamental in $ {L_2}(R)$, and find a representation for those functions which are in the closure of its linear span. Some theorems concerning degree of approximation are also proved.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0550509-2
Keywords: Approximation by sequences of translates, entire functions, Fourier inversion
Article copyright: © Copyright 1980 American Mathematical Society