|
Infinite type homeomorphisms of the circle and convergence of Fourier series
Author(s):
Antônio
Zumpano
Journal:
Trans. Amer. Math. Soc.
350
(1998),
4023-4040.
MSC (1991):
Primary 42A20;
Secondary 26A45
Retrieve article in:
PDF
This article is available free of charge
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:
- 1.
- Kahane, J. P. - Quatre Leçons sur les Homéomorphismes du Circle et les Series de Fourier. Topics in Modern Harmonic Analysis, Proceedings of a seminar held in Torino and Milano, May - June 1982, vol. II, Roma, 1983. MR 85k:42012
- 2.
- Stein, E. M. and Wainger, S. - The Estimation of an Integral Arising in Multiplier Transformations, Studia Math. 35 (1970), 101 - 104. MR 42:904
- 3.
- Stein, E. M. - Oscillatory Integral in Fourier Analysis, Beijing Lectures in Harmonic Analysis, edited by E. M. Stein, Princeton University Press. (1986), 307 - 355. MR 88g:42022
- 4.
- Nagel, A., Vance, J., Wainger, S. and Weinberg, D. - Hilbert Transforms for Convex Curves, Duke Mathematical Journal. Vol. 50 (1983), 735 - 744. MR 85a:42025
- 5.
- Santos Zumpano, A. - Homeomorphisms Of The Circle And Fourier Series, Ph.D thesis - University of Wisconsin - Madison, May 1987.
Similar Articles:
Retrieve articles in Transactions of the American Mathematical Society
with MSC
(1991):
42A20,
26A45
Retrieve articles in all Journals with MSC
(1991):
42A20,
26A45
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
DOI:
10.1090/S0002-9947-98-02076-5
PII:
S 0002-9947(98)02076-5
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
Copyright of article:
Copyright
1998,
American Mathematical Society
|
Comments: webmaster@ams.org