the uncertainty principle

@article{Fefferman1983theUP,
  title={the uncertainty principle},
  author={Charles Fefferman},
  journal={Bulletin of the American Mathematical Society},
  year={1983},
  volume={9},
  pages={129-206}
}
  • C. Fefferman
  • Published 1 September 1983
  • Mathematics
  • Bulletin of the American Mathematical Society
On considere l'existence et la regularite des solutions d'equations aux derivees partielles, la construction de solutions fondamentales explicites et les valeurs propres d'operateurs de Schrodinger 
Fundamental solutions for second order subelliptic operators
Estimation de la solution fondamentale d'un operateur aux derivees partielles, lineaire, du second ordre sur une variete compacte avec une mesure reguliere
Operateijrs sous-elliptiques et regularite des solutions d'equations aux derivees partielles non lineaires du second ordre en deux variablfs
On demontre que la condition geometrique B −Δ (x,ρ)CB L (x,c,ρe); ∀x∈Ω, ρ∈]0,1[, est suffisante pour avoir une estimation sous-elliptique pour un operateur differentiel lineaire a coefficient C 2
Weighted norm inequalities for potentials with applications to Schrödinger operators, Fourier transforms, and Carleson measures
On donne une nouvelle caracterisation de l'inegalite de trace pour des operateurs potentiel et on l'utilise pour affiner des resultats sur la distribution des valeurs propres des operateurs de
LPEstimates for fractional integrals and sobolev inequalities with applications to schrödinger operators
On considere le probleme de la fonction a deux poids pour L P pour l'inegalite de Poincare, l'inegalite de Sobolev et des integrales fractionnaires. On donne des applications des inegalites aux
Carleman inequalities for the Dirac and Laplace operators and unique continuation
On demontre les meilleures inegalites de type Carleman possibles dans le cas de l'operateur de Dirac. On obtient la propriete de prolongement unique pour D+V, ou V∈L loc γ(R n ), γ=(3n-2)/2, (n≥3)
The spectrum of the Schrödinger operator
On decrit le spectre negatif de l'operateur de Schrodinger avec un potentiel singulier. On determine la valeur exacte du fond du spectre et on etablit une double estimation
Nonclassical eigenvalue asymptotics for operators of Schrödinger type
On considere des operateurs de la forme A=−⊇•ρ⊇+V(x) sur R n , ou la metrique ρ=(ρ ij (x))≥0 et le potentiel v(x)≥0. On etudie la fonction de denombrement des valeurs propres par un calcul
A characterization of two weight norm inequalities for fractional and Poisson integrals
Caracterisation de deux inegalites de normes ponderees pour les integrales fractionnaires et de Poisson. Applications aux operateurs differentiels elliptiques degeneres
Un majorant du nombre des valeurs propres négatives correspondantes à l’opérateur de Schrödinger généralisé.@@@An upper bound on the number of negative eigenvalues
On donne une borne superieur du nombre des valeurs propres negatives de l'operateur de Schrodinger generalise, cette borne est donnee en fonction d'un nombre fini de cube dyadiques minimaux.
Lp uncertainty principles on Sturm–Liouville hypergroups
We use the Fourier analysis associated to a singular second-order differential operator Δ, and prove a continuous-time principle for the Lp theory.
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