Nazarov's uncertainty principles in higher dimension

  • Authors:

  • Philippe Jaming

  • Affiliations:

  • Faculté des Sciences, MAPMO-Fédération Denis Poisson, Université d'Orléans, BP 6759, F 45067 Orléans Cedex 2, France

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2007

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Abstract

In this paper we prove that there exists a constant C such that, if S,@S are subsets of R^d of finite measure, then for every function f@?L^2(R^d),@!"R"^"d|f(x)|^2dx==1 a result of Nazarov [Local estimates for exponential polynomials and their applications to inequalities of the uncertainty principle type, Algebra i Analiz 5 (1993) 3-66 (in Russian); translation in St. Petersburg Math. J. 5 (1994) 663-717] in dimension d=1.