Résumé
On montre que si L est une forme linéaire régulière et semi-classique, alors la forme u=L + λδc où c ε C est quelconque, est encore régulière et semi-classique pour tout λ ε C en dehors d'un ensemble dénombrable de valeurs singulières. On donne l'équation différentielle linéaire du second ordre vérifiée par chaque polynôme de la suite orthogonale associée à u.
Abstract
We show that, if L is a regular, semi-classical functional, then u=L + λδc where c ε C, is also regular and semi-classical for every complex λ, except for a discret set. We give the second order linear differential equation satisfied by each polynomial of the orthogonal sequence associated with u.
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Marcellan, F., Maroni, P. Sur l'adjonction d'une masse de Dirac á une forme régulière et semi-classique. Annali di Matematica pura ed applicata 162, 1–22 (1992). https://doi.org/10.1007/BF01759996
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DOI: https://doi.org/10.1007/BF01759996