heisenberg uncertainty principle fourier transform

The more concentrated a signal is in the time domain, the more spread out it is in the frequency domain. There is a closely related principle in Fourier analysis that says a function and its Fourier transform cannot both be localized. The product of the uncertainties in the two quantities has a lower bound. Accepted: March 2015.Heisenberg’s uncertainty principle says there is a limit to how well you can know both the position and momentum of anything at the same time. Watson, A treatise on the theory of Bessel functions, Cambridge univ. Vu Kim Tuan, Uncertainty principle for the Hankel transform. Trimèche, Inversion of the Lions transmutation operator using genaralized wavelets, Appl. Trimèche, Transformation intégrale de Weyl et théorème de Paley-Wiener associés á un opérateur différentiel singulier sur (0,+∞), J. Shanon, A mathematical theory of communication, Bell System Tech. Voit, An uncertaintly principle for the Hankel transforms, American Mathematical Society, 127 (1) (1999), 183- 194. Lebedev, Special Functions and Their Applications, Dover publications, New-York 1972. Hirschman, Variation diminishing Hankel transforms, J. Hardy, A theorem concerning Fourier transform, J. Sitaram, The uncertainty principle: a mathematical survey, J. Folland, Real analysis modern thechniques and their applications, Pure and Applied Mathematics, John Wiley and Sons, New York 1984. Fitouhi, Inégalité de Babenko et inégalité logarithmique de Sobolev pour l’opérateur de Bessel, C. Erdélyi, Asymptotic expansions, Dover publications, New-York 1956.

Erdélyi et al., Tables of integral transforms, Mc Graw-Hill Book Compagny., Vol.2, New York 1954. Price, Generalizations of Heisenberg inequality in Harmonic analysis, (Cortona, 1982), Lecture Notes in Math., 992 (1983) 443≤49. Jaming, Hermite functions and uncertainty priciples for the Fourier and the widowed Fourier transforms, Rev. VonWaldenfels, Lecture Notes in Mathematics, 1136 (1985) 90- 103.

Bialynicki-Birula, Entropic uncertainty relations in quantum mechanics, quantum probability and applications II, Eds. Beurling, The collected works of Arne Beurling, Birkhäuser, Vol.1-2, Boston 1989. Beckner, Pitt’s inequality and the uncertainty principle, Proc. Beckner, Inequalities in Fourier analysis, Ann. Keywords and Phrases: Uncertainty principle, Hausdorff-Young inequality, entropy, Hankel transformĢ010 AMS Mathematics Subject Classification: 43A32, 42B25. Además probamos que podemos obtener la desigualdad de Heisenberg-Pauli-Weyl relacionada con la misma transformada de Hankel. Usamos la desigualdad de Hausdorff-Young para la transformada de Hankel para probar el principio de incertidumbre en términos de la entropía. Next, we show that we can obtain the Heisenberg- Pauli-Weyl inequality related to the same Hankel transform. use the Hausdorff-Young inequality for the Hankel transform to prove the uncertainly principle in terms of entropy. An other uncertainty principle for the Hankel transformĭépartement de Mathématiques et d’Informatique, Institut national des sciences appliquées et de Thechnologie, Centre Urbain Nord BP 676 - 1080 Tunis cedex, Tunisia.

Heisenberg uncertainty principle fourier transform