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The Gibbs Phenomenon for Generalized Taylor and Euler Transforms

Published online by Cambridge University Press:  20 November 2018

Robert E. Powell  and
Richard A. Shoop
Robert E. Powell
Affiliation:
Kent State University, Kent, Ohio
Richard A. Shoop
Affiliation:
Kent State University, Kent, Ohio
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Let f be a real-valued function satisfying the Dirichlet conditions in a neighborhood of x = x0, at which point f has a jump discontinuity. If {Sn(x)} is the sequence of partial sums of the Fourier series of f at x, then ﹛Sn(x)﹜ cannot converge uniformly at x — x0. Moreover, for any number , there exists a sequence ﹛tn﹜, where tn → x0 and

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 2 , 01 April 1975 , pp. 384 - 395
Copyright
Copyright © Canadian Mathematical Society 1975

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