Maximal values for the simultaneous number of null components of a vector and its Fourier transform

• Alberto Debernardi Pinos ^[1]
  1. [1] Centre de Recerca Matematica

     Centre de Recerca Matematica

     Sardañola del Vallés, España

     
• Localización: Reports@SCM: an electronic journal of the Societat Catalana de Matemàtiques, ISSN-e 2385-4227, Vol. 2, Nº. 1, 2016, págs. 1-10
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen
  • English

    Motivated by the uncertainty principle, the purpose of this work is to find the maximal value of simultaneous number of null components of a vector and its discrete Fourier transform. In other words if we denote W and Z the number of null components of a vector x and its Fourier transform, respectively, the uncertainty principle ensures that W and Z are inversely proportional. We study the best possible balance between those two numbers.

  • català

    Motivat pel principi d’incertesa, el propòsit d’aquest treball és el de trobar el valor dels nombres L(N) = maxx∈CN\{0}min{Z(x),Z(ˆx)}, on ˆxiZ(x) denoten la transformada de Fourier discreta i el nombre de components nul·les de x,respectivament. Dit d’una altra manera, ja que el principi d’incertesa ens assegura que Z(x) és inversament proporcional a Z(ˆx), estudiem el millor balanç que hi pot haver entre aquests dos nombres.

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