Comptes Rendus
no. 7
Physics/Mathematical physics, theoretical physics
Orthogonal polynomial sets with finite codimensions
[Polynômes orthogonaux contraints.]

Présenté par : Roger Balian

Bertrand G. Giraud1 ; M.L. Mehta1 ; A. Weiguny2
1 Service de physique théorique, CNRS, CE Saclay, 91191 Gif/Yvette, France
2 Institut für Theoretische Physik, Univeristät Münster, Germany
Comptes Rendus. Physique, Ice: from dislocations to icy satellites, Volume 5 (2004) no. 7, pp. 781-787.

Nous définissons des ensembles des polynômes orthogonaux sous des contraintes diverses. C'est notamment les cas d'une généralisation de polynômes d'Hermite, contraintes par une moyenne de zéro, pour la fonctionnelle de Hohenberg–Kohn. Ils permettent le calcul des perturbations de potentiel qui engendrent strictement la même forme pour les perturbations de densité.

We define sets of orthogonal polynomials which lack one or several degrees, because of a finite number of constraints. In particular, we are interested in a generalization of Hermite polynomials, governed by a constraint of zero average. These are of interest, for example, for the study of the Hohenberg–Kohn functional. In particular, they allow the calculation of potential perturbations which generate strictly proportional density perturbations.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crhy.2004.09.017

Bertrand G. Giraud 1 ; M.L. Mehta 1 ; A. Weiguny 2

1 Service de physique théorique, CNRS, CE Saclay, 91191 Gif/Yvette, France
2 Institut für Theoretische Physik, Univeristät Münster, Germany 
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Bertrand G. Giraud; M.L. Mehta; A. Weiguny. Orthogonal polynomial sets with finite codimensions. Comptes Rendus. Physique, Ice: from dislocations to icy satellites, Volume 5 (2004) no. 7, pp. 781-787. doi : 10.1016/j.crhy.2004.09.017. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2004.09.017/

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[4] R. Berg; L. Wilets; W. Kohn; L.J. Sham Phys. Rev. A, LXVIII (1955) no. 4, p. 229

  • B. G. Giraud Density functionals in the laboratory frame, Physical Review C, Volume 77 (2008) no. 1 | DOI:10.1103/physrevc.77.014311
  • Jean-Marie Normand Block orthogonal polynomials: I. Definitions and properties, Journal of Physics A: Mathematical and Theoretical, Volume 40 (2007) no. 10, p. 2341 | DOI:10.1088/1751-8113/40/10/009
  • Jean-Marie Normand Block orthogonal polynomials: II. Hermite and Laguerre standard block orthogonal polynomials, Journal of Physics A: Mathematical and Theoretical, Volume 40 (2007) no. 10, p. 2371 | DOI:10.1088/1751-8113/40/10/010
  • B.G. Giraud; K. Katō; A. Ohnishi; S.M.A. Rombouts Existence of density functionals for excited states and resonances, Physics Letters B, Volume 652 (2007) no. 2-3, p. 69 | DOI:10.1016/j.physletb.2007.06.071
  • B G Giraud Constrained orthogonal polynomials, Journal of Physics A: Mathematical and General, Volume 38 (2005) no. 33, p. 7299 | DOI:10.1088/0305-4470/38/33/006

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