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Proceedings of the American Mathematical Society

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

 

 

Representation of a crinkled arc


Author: Richard A. Vitale
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
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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:

$\displaystyle f(t) = \sqrt 2 \sum\limits_{n = 1}^\infty {{x_n}\tfrac{{\sin (n -... ...yle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}})\pi }}} ,$

where $ \{ {x_n}\} $ is an orthonormal set.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0388056-1
Keywords: Crinkled arc, Brownian motion, Karhunen-Loève expansion
Article copyright: © Copyright 1975 American Mathematical Society