Geodesic
One cannot hear the winding number
Journal of the European Mathematical Society, Tome 9 (2007) no. 4, pp. 637-658

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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.
DOI : 10.4171/jems/91
Classification : 42-XX, 55-XX, 00-XX
Keywords: Winding number, Fourier coefficients, Pauli partners, random Fourier series 
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     author = {Jean Bourgain and Gady Kozma},
     title = {One cannot hear the winding number},
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     year = {2007},
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Jean Bourgain; Gady Kozma. One cannot hear the winding number. Journal of the European Mathematical Society, Tome 9 (2007) no. 4, pp. 637-658. doi: 10.4171/jems/91

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