The kechris–woodin rank is finer than the zalcwasser rank

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

For each differentiable function f on the unit circle, the Kechris Woodin rank measures the failure of continuity of the derivative function f' while the Zalcwasser rank measures how close the Fourier series of f is to being a uniformly convergent series. We show that the Kechris-Woodin rank is finer than the Zalcwasser rank. Roughly speaking, small ranks mean the function is well behaved and big ranks imply bad behavior. For each countable ordinal, we explicitly construct a continuous function with everywhere convergent Fourier series such that the Zalcwasser rank of the function is bigger than the ordinal.

Original languageEnglish
Pages (from-to)4471-4484
Number of pages14
JournalTransactions of the American Mathematical Society
Volume347
Issue number11
DOIs
Publication statusPublished - 1995 Nov

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Fourier series
Unit circle
Derivatives
Differentiable
Countable
Continuous Function
Imply
Derivative
Series

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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abstract = "For each differentiable function f on the unit circle, the Kechris Woodin rank measures the failure of continuity of the derivative function f' while the Zalcwasser rank measures how close the Fourier series of f is to being a uniformly convergent series. We show that the Kechris-Woodin rank is finer than the Zalcwasser rank. Roughly speaking, small ranks mean the function is well behaved and big ranks imply bad behavior. For each countable ordinal, we explicitly construct a continuous function with everywhere convergent Fourier series such that the Zalcwasser rank of the function is bigger than the ordinal.",
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The kechris–woodin rank is finer than the zalcwasser rank. / Ki, Haseo.

In: Transactions of the American Mathematical Society, Vol. 347, No. 11, 11.1995, p. 4471-4484.

Research output: Contribution to journalArticle

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