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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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Representation of a crinkled arc
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by Richard A. Vitale PDF
Proc. Amer. Math. Soc. 52 (1975), 303-304 Request permission

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.
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Additional 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