One cannot hear the winding number

  • Jean Bourgain

    Institute for Advanced Study, Princeton, United States
  • Gady Kozma

    Weizmann Institute of Science, Rehovot, Israel


We construct an example of two continuous maps f and g of the circle to itself with the same absolute value of the Fourier transform but with different winding numbers, answering a question of Brezis.

Cite this article

Jean Bourgain, Gady Kozma, One cannot hear the winding number. J. Eur. Math. Soc. 9 (2007), no. 4, pp. 637–658

DOI 10.4171/JEMS/91