An other uncertainty principle for the Hankel transform

• Chirine Chettaoui ^[1]
  1. [1] Institut national des sciences appliquées et de Thechnologie Département de Mathématiques et d’Informatique
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 17, Nº. 2, 2015, págs. 15-30
• Idioma: inglés
• DOI: 10.4067/S0719-06462015000200002
• Enlaces
  • Texto completo
• Resumen
  • español

    Usamos la desigualdad de Hausdorff-Young para la transformada de Hankel para probar el principio de incertidumbre en términos de la entropía. Además probamos que podemos obtener la desigualdad de Heisenberg-Pauli-Weyl relacionada con la misma transformada de Hankel.

  • English

    We use the Hausdorff-Young inequality for the Hankel transform to prove the uncertainly principle in terms of entropy. Next, we show that we can obtain the Heisenberg- Pauli-Weyl inequality related to the same Hankel transform.

• Referencias bibliográficas
  • Beckner, W. (1975). Inequalities in Fourier analysis. Ann. of Math. 102. 159-182
  • Beckner, W. (1995). Pitt’s inequality and the uncertainty principle. Proc. Amer. Math. Soc. 1897-1905
  • Beurling, A. (1989). The collected works of Arne Beurling. Birkhäuser. 12.
  • Bialynicki-Birula, I,Accardi, L,VonWaldenfels, W. (1985). Lecture Notes in MathematicsEntropic uncertainty relations in quantum mechanics,...
  • Bonami, A,Demange, B,Jaming, P. (2003). Hermite functions and uncertainty priciples for the Fourier and the widowed Fourier transforms. Rev....
  • Cowling, M.G,Price, J. F. (1983). Generalizations of Heisenberg inequality in Harmonic analysis: Cortona, 1982. Lecture Notes in Math. 992....
  • Erdélyi, A. (1954). Tables of integral transforms. Mc Graw-Hill Book Compagny. New York.
  • Erdélyi, A. (1956). Asymptotic expansions. Dover publications. New-York.
  • Fitouhi, A. (1987). Inégalité de Babenko et inégalité logarithmique de Sobolev pour l’opérateur de Bessel. C. R. Acad. Sci. Paris. 305. 877-880
  • Folland, G. B. (1984). Real analysis modern thechniques and their applications, Pure and Applied Mathematics. John Wiley and Sons. New York....
  • Folland, G. B,Sitaram, A. (1997). The uncertainty principle: a mathematical survey. J. Fourier Anal. Appl. 3. 207-238
  • Hardy, G. H. (1933). A theorem concerning Fourier transform. J. London. Math. Soc. 8. 227-231
  • Hirschman, I. I. (1957). A note on entropy. Amer. J. Math. 79. 152-156
  • Hirschman, I. I. (1960). Variation diminishing Hankel transforms. J. Anal. Math. 8. 307-336
  • Lebedev, N. N. (1972). Special Functions and Their Applications. Dover publications. New-York.
  • Morgan, G. W. (1934). A note on Fourier transforms. J. London. Math. Soc. 9. 178-192
  • Rösler, M,Voit, M. (1999). An uncertaintly principle for the Hankel transforms. American Mathematical Society. 127. 183-194
  • Shanon, C. (1948). A mathematical theory of communication. Bell System Tech. J. 27. 379-423
  • Trimèche, K. (1981). Transformation intégrale de Weyl et théorème de Paley-Wiener associés á un opérateur différentiel singulier sur (0,+∞)....
  • Trimèche, K. (1997). Inversion of the Lions transmutation operator using genaralized wavelets. Appl. Comput. Harmon. Anal. 4. 97-112
  • Tuan, Vu Kim. (2007). Uncertainty principle for the Hankel transform. Integral Transforms Spec. Funct. 18. 369-381
  • Watson, G. N. (1959). A treatise on the theory of Bessel functions. 2. Cambridge univ. Press. Cambridge.