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Proceedings of the American Mathematical Society

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Completeness of $ \{{\rm sin}\ nx+Ki$ $ {\rm cos}\ nx\}$


Author: Jonathan I. Ginsberg
Journal: Proc. Amer. Math. Soc. 29 (1971), 291-293
MSC: Primary 42.17
DOI: https://doi.org/10.1090/S0002-9939-1971-0276679-6
MathSciNet review: 0276679
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Abstract: Let $ {\mathbf{C}}[ {a,b} ]$ be the space of continuous functions on the interval $ [ {a,b} ]$. It is shown that the set of functions $ \{ {\sin nx + Ki\cos nx} \}_{n = 1}^\infty ,K \ne \pm 1$, is incomplete in $ {\mathbf{C}}[ {0,\pi + a} ],a > 0$.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0276679-6
Keywords: Completeness, $ {\mathbf{C}}[0,\pi + a]$
Article copyright: © Copyright 1971 American Mathematical Society