Nazarov's uncertainty principles in higher dimension

• Autores: Philippe Jaming
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 149, Nº 1, 2007, págs. 30-41
• Idioma: inglés
• DOI: 10.1016/j.jat.2007.04.005
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this paper we prove that there exists a constant C such that, if S,S are subsets of of finite measure, then for every function ,where is the Fourier transform of f and w(S) is the mean width of S. This extends to dimension d1 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.

• Referencias bibliográficas
  • W.O. Amrein and A.M. Berthier, On support properties of Lp-functions and their Fourier transforms, J. Funct. Anal. 24 (1977) 258–267.
  • M. Benedicks, On Fourier transforms of functions supported on sets of finite Lebesgue measure, J. Math. Anal. Appl. 106 (1985) 180–183.
  • A. Bonami, B. Demange, A survey on the uncertainty principle for quadratic forms, Collectanea Math. (2006) 1–36 (e-print).
  • B. Demange, Principes d’incertitude associés à des formes quadratiques non dégénérées, Thèse de l’université d’Orléans, 2004.
  • B. Demange, Inégalités d’incertitude associées à des fonctions homogènes, C. R. Math. Acad. Sci. Paris 340 (2005) 709–714.
  • G.B. Folland, A. Sitaram, The uncertainty principle, a mathematical survey, J. Fourier Anal. Appl. 3 (1997) 207–238.
  • N. Fontes-Merz, A multidimensional version of Turán’s lemma, J. Approx. Theory 140 (2006) 27–30.
  • V. Havin, B. Jöricke, The Uncertainty Principle in Harmonic Analysis, Springer, Berlin, 1994.
  • V. Havin, B. Jöricke, The uncertainty principle in harmonic analysis, Commutative harmonic analysis, vol. III, 177–259, 261–266, Encyclopaedia...
  • O. Korenyikine, Some results related to the Logvinenko-Sereda theorem, Proc. Amer. Math. Soc. 129 (2001) 3037–3047.
  • V.N. Logvinenko, Ju.F. Sereda, Equivalent norms in spaces of entire functions of exponential type, Teor. FunkciiFunkcional. Anal. i Priložen....
  • F.L. Nazarov, Local estimates for exponential polynomials and their applications to inequalities of the uncertainty principle type, Algebra...
  • B. Paneah, On certain problems of harmonic analysis, Soviet Math. Dokl. 3 (1962) 239–242.
  • B. Paneah, Support-dependent weighted norm estimates for Fourier transforms, J. Math. Anal. Appl. 189 (1995) 552–574.
  • B. Paneah, Support-dependent weighted norm estimates for Fourier transforms II, Duke Math. J. 92 (1998) 35–353.
  • C. Shubin, R. Vakilian, T. Wolff, Some harmonic analysis questions suggested by Anderson–Bernoulli models, Geom. Funct. Anal. 8 (1998) 932–964.
  • P. Turán, Eine neue Methode in der Analyse und deren Anwendungen, Akadémi Kiadó, Budapest, 1953.