One cannot hear the winding number
Jean Bourgain
Institute for Advanced Study, Princeton, United StatesGady Kozma
Weizmann Institute of Science, Rehovot, Israel
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Abstract
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