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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Infinite type homeomorphisms of the circle
and convergence of Fourier series

Author: Antônio Zumpano
Journal: Trans. Amer. Math. Soc. 350 (1998), 4023-4040
MSC (1991): Primary 42A20; Secondary 26A45
MathSciNet review: 1451619
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the problem of convergence of Fourier series when we make a change of variable. Under a certain reasonable hypothesis, we give a necessary and sufficient condition for a homeomorphism of the circle to transform absolutely convergent Fourier series into uniformly convergent Fourier series.

References [Enhancements On Off] (What's this?)

  • 1. Jean-Pierre Kahane, Quatre leçons sur les homéomorphismes du cercle et les séries de Fourier, Topics in modern harmonic analysis, Vol. I, II (Turin/Milan, 1982), Ist. Naz. Alta Mat. Francesco Severi, Rome, 1983, pp. 955–990 (French). MR 748889
  • 2. Elias M. Stein and Stephen Wainger, The estimation of an integral arising in multiplier transformations., Studia Math. 35 (1970), 101–104. MR 0265995
  • 3. E. M. Stein, Oscillatory integrals in Fourier analysis, Beijing lectures in harmonic analysis (Beijing, 1984) Ann. of Math. Stud., vol. 112, Princeton Univ. Press, Princeton, NJ, 1986, pp. 307–355. MR 864375
  • 4. Alexander Nagel, James Vance, Stephen Wainger, and David Weinberg, Hilbert transforms for convex curves, Duke Math. J. 50 (1983), no. 3, 735–744. MR 714828, 10.1215/S0012-7094-83-05036-6
  • 5. Santos Zumpano, A. - Homeomorphisms Of The Circle And Fourier Series, Ph.D thesis - University of Wisconsin - Madison, May 1987.

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Additional Information

Antônio Zumpano
Affiliation: Departamento de Matematica, Universidade Federal de Minas Gerais, Caixa Postal 702, 30.123-970 Belo Horizonte MG, Brazil

Keywords: Oscillatory integral, Fourier analysis, Fourier series, homeomorphism of the circle
Received by editor(s): November 6, 1994
Received by editor(s) in revised form: October 23, 1996
Article copyright: © Copyright 1998 American Mathematical Society