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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Some stability theorems for nonharmonic Fourier series
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by Robert M. Young PDF
Proc. Amer. Math. Soc. 61 (1976), 315-319 Request permission

Abstract:

The theory of nonharmonic Fourier series in ${L^2}( - \pi ,\pi )$ is concerned with the completeness and expansion properties of sets of complex exponentials $\{ {e^{i{\lambda _n}t}}\}$. It is well known, for example, that the completeness of the set $\{ {e^{i{\lambda _n}t}}\}$ ensures that of $\{ {e^{i{\mu _n}t}}\}$ whenever $\sum {|{\lambda _n} - {\mu _n}| < \infty }$. In this note we establish two results which guarantees that if $\{ {e^{i{\lambda _n}t}}\}$ is a Schauder basis for ${L^2}( - \pi ,\pi )$, then $\{ {e^{i{\mu _n}t}}\}$ is also a Schauder basis whenever $\{ {\mu _n}\}$ is “sufficiently close” to $\{ {\lambda _n}\}$.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 61 (1976), 315-319
  • MSC: Primary 42A64
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0425499-2
  • MathSciNet review: 0425499