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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Representation of a crinkled arc
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by Richard A. Vitale
Proc. Amer. Math. Soc. 52 (1975), 303-304
DOI: https://doi.org/10.1090/S0002-9939-1975-0388056-1

Abstract:

Johnson [A crinkled arc, Proc. Amer. Math. Soc. 25 (1970), 375-376] has shown that under suitable normalizations all crinkled arcs are unitarily equivalent. Using this result, we find a general series expansion for a crinkled arc: \[ f(t) = \sqrt {2} \sum _{n=1}^\infty x_n \tfrac {\sin (n - 1/2)\pi t}{(n - 1/2)\pi } , \] where $\{ {x_n}\}$ is an orthonormal set.
References
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Bibliographic Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 52 (1975), 303-304
  • MSC: Primary 46C10
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0388056-1
  • MathSciNet review: 0388056