Infinite type homeomorphisms of the circle and convergence of Fourier series
HTML articles powered by AMS MathViewer
- by Antônio Zumpano PDF
- Trans. Amer. Math. Soc. 350 (1998), 4023-4040 Request permission
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
- 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
- Elias M. Stein and Stephen Wainger, The estimation of an integral arising in multiplier transformations, Studia Math. 35 (1970), 101–104. MR 265995, DOI 10.4064/sm-35-1-101-104
- 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
- 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, DOI 10.1215/S0012-7094-83-05036-6
- Santos Zumpano, A. - Homeomorphisms Of The Circle And Fourier Series, Ph.D thesis - University of Wisconsin - Madison, May 1987.
Additional Information
- Antônio Zumpano
- Affiliation: Departamento de Matematica, Universidade Federal de Minas Gerais, Caixa Postal 702, 30.123-970 Belo Horizonte MG, Brazil
- Email: zumpano@mat.ufmg.br
- Received by editor(s): November 6, 1994
- Received by editor(s) in revised form: October 23, 1996
- © Copyright 1998 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 350 (1998), 4023-4040
- MSC (1991): Primary 42A20; Secondary 26A45
- DOI: https://doi.org/10.1090/S0002-9947-98-02076-5
- MathSciNet review: 1451619