the uncertainty principle

  title={the uncertainty principle},
  author={Charles Fefferman},
  journal={Bulletin of the American Mathematical Society},
  • 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.


On positivity of pseudo-differential operators.
  • C. Fefferman, D. H. Phong
  • Mathematics, Medicine
    Proceedings of the National Academy of Sciences of the United States of America
  • 1978
New lower bounds for pseudo-differential operators with non-negative symbols are obtained, thus providing a sharper form of Gårding's inequality.
Functional integration and quantum physics
Introduction The basic processes Bound state problems Inequalities Magnetic fields and stochastic integrals Asymptotics Other topics References Index Bibliographic supplement Bibliography.
Symplectic geometry and positivity of pseudo-differential operators.
  • C. Fefferman, D. H. Phong
  • Mathematics, Medicine
    Proceedings of the National Academy of Sciences of the United States of America
  • 1982
Positivity for pseudo-differential operators under a condition that is essentially also necessary is established under a microlocalization procedure and a geometric lemma.
On integral representations for the Neumann operator.
  • D. H. Phong
  • Mathematics, Medicine
    Proceedings of the National Academy of Sciences of the United States of America
  • 1979
A new class of singular integral operators arises that are infinitely smoothing in the interior and preserve singular supports at the boundary and whose kernels are products of isotropic kernels with parabolic ones.
The spectral function of an elliptic operator
In this paper we shall obtain the best possible estimates for the remainder term in the asymptotic formula for the spectral function of an arbitrary elliptic (pseudo-)differential operator. This is
A class of bounded pseudo-differential operators.
Pseudo-differential operators of order -M and type rho, delta(1), delta(2) are shown to be bounded in L(2) provided that 0 </= rho </= delta(1) < 1, 0 </= rho </= delta(2) < 1, and [Formula: see
Strictly pseudoconvex domains in $C^n$
The theory which we have developed so far will be expanded in two ways: 1° In this chapter we shall use the Cauchy-Fantappie calculus to transform the Bochner-Martinelli kernel into a kernel adapted
On the asymptotic eigenvalue distribution of a pseudo-differential operator.
  • C. Fefferman, D. H. Phong
  • Mathematics, Medicine
    Proceedings of the National Academy of Sciences of the United States of America
  • 1980
A description of the number N(K) of eigenvalues less than K for a pseudo-differential operator with positive symbol is given in terms of the number of unit cubes canonically imbedded in the subset of
Harmonic Integrals on Strongly Pseudo-Convex Manifolds: II
In this paper we prove the basic existence and regularity theorems for the a-Neumann problem (see Theorems 6.6 and 6.14). The results presented here were outlined by the author in [8]. In Part I of