Une fonction eulerienne formelle

Autores: G. Cauchon
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 46, Fasc. 1-2, 1995 (Ejemplar dedicado a: Professor Paul Dubreil (In memoriam )), págs. 49-56
Idioma: francés
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Resumen
- In this paper, we state and prove a formal version of a factorisation theorem, a particular case of which, due to A. Unterberger [2], concerns the operator $p^2 + q^2 -\lambda^2$ where $\lambda\in ]1/2,+\infty[$ and $p, q$ are operators on the Poincaré half plane $\{z\in\mathbb{ C}\vert Re(z) > 0\}$ , such that $[p, q] = q$. \newline As this factorisation involves operators in the form $\Gamma(ap+b)$ (defined in the sens of the spectral theory), where $\Gamma$ is the well known Euler function and $(a, b)\in (\mathbb{C}\setminus \{0\})\times\mathbb{C}$, we construct a formal version for those operators, and explain why this construction cannot be done in terms of formal series in $p$.
Referencias bibliográficas
- A. Borel et al., Algebraic D-Modules, Perspectives in Mathematics, vol. 2, Academic Press Inc., Orlando, 1987.
- A. Unterberger, Calcul de Weyl construit sur une autre relation de commutation que celle d’Heisenberg. Manuscrit non publié, Département de...