Winding numbers and Fourier series
Informatics and Automation, Modern problems of mathematics, Tome 273 (2011), pp. 207-211.

Voir la notice de l'article provenant de la source Math-Net.Ru

This is an expository paper on a topic of classical analysis arising from the BMO-theory of topological degree (Brezis–Nirenberg, 1995). We sketch the history of the subject and some of its recent developments.
@article{TRSPY_2011_273_a7,
     author = {Jean-Pierre Kahane},
     title = {Winding numbers and {Fourier} series},
     journal = {Informatics and Automation},
     pages = {207--211},
     publisher = {mathdoc},
     volume = {273},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2011_273_a7/}
}
TY  - JOUR
AU  - Jean-Pierre Kahane
TI  - Winding numbers and Fourier series
JO  - Informatics and Automation
PY  - 2011
SP  - 207
EP  - 211
VL  - 273
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2011_273_a7/
LA  - en
ID  - TRSPY_2011_273_a7
ER  - 
%0 Journal Article
%A Jean-Pierre Kahane
%T Winding numbers and Fourier series
%J Informatics and Automation
%D 2011
%P 207-211
%V 273
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2011_273_a7/
%G en
%F TRSPY_2011_273_a7
Jean-Pierre Kahane. Winding numbers and Fourier series. Informatics and Automation, Modern problems of mathematics, Tome 273 (2011), pp. 207-211. http://geodesic.mathdoc.fr/item/TRSPY_2011_273_a7/

[1] Bourgain J., Kahane J.-P., “Sur les séries de Fourier des fonctions continues unimodulaires”, Ann. Inst. Fourier., 60:4 (2010), 1201–1214 | DOI | MR | Zbl

[2] Bourgain J., Kozma G., “One cannot hear the winding number”, J. Eur. Math. Soc., 9 (2007), 637–658 | DOI | MR | Zbl

[3] Brezis H., “New questions related to the topological degree”, The unity of mathematics, In honour of the 90th birthday of I.M. Gelfand, Prog. Math., 244, Birkhäuser, Boston, 2006, 137–154 | DOI | MR

[4] Brezis H., Coron J.-M., “Large solutions for harmonic maps in two dimensions”, Commun. Math. Phys., 92 (1983), 203–215 | DOI | MR | Zbl

[5] Brezis H., Nirenberg J., “Degree theory and BMO. I: Compact manifolds without boundaries”, Sel. math., 1 (1995), 197–263 | DOI | MR | Zbl

[6] Hardy G.H., Divergent series, Clarendon Press, Oxford, 1949 ; Chelsea, New York, 1991 | MR | Zbl | Zbl

[7] Kahane J.-P., “Sur l'équation fonctionnelle $\int _\pi (\psi (t+s)-\psi (s))^3ds=\sin t$”, C. r. Math. Acad. sci. Paris, 341 (2005), 141–145 | DOI | MR | Zbl

[8] Kahane J.-P., “Winding numbers and summation processes”, Complex Var. and Elliptic Equat., 55 (2010), 911–922 | DOI | MR | Zbl

[9] Korevaar J., “On a question of Brézis and Nirenberg concerning the degree of circle maps”, Sel. math., 5 (1999), 107–122 | DOI | MR | Zbl

[10] Kuttner B., “The relation between Riemann and Cesàro summability”, Proc. London Math. Soc. Ser. 2, 38 (1935), 273–283 | DOI | MR

[11] Zygmund A., Trigonometric series, v. 1, Cambridge Univ. Press, Cambridge, 1959 | MR | Zbl

[12] Zygmund A., “Sur la dérivation des séries de Fourier”, Bull. Acad. Pol. A, 1924, 243–249 | Zbl