Rational Hadamard products via Quantum Diagonal Operators

Gérard Henry Edmond Duchamp (1) , Silvia Goodenough (1) , Karol A. Penson (2)

1 LIPN - Laboratoire d'Informatique de Paris-Nord
2 LPTMC - Laboratoire de Physique Théorique de la Matière Condensée

We use the remark that, through Bargmann-Fock representation, diagonal operators of the Heisenberg-Weyl algebra are scalars for the Hadamard product to give some properties (like the stability of periodic fonctions) of the Hadamard product by a rational fraction. In particular, we provide through this way explicit formulas for the multiplication table of the Hadamard product in the algebra of rational functions in $\C[[z]]$.

Mots clés: Heisenberg-Weyl algebra; Diagonal Operators

Domaines: Calcul formel [cs.SC]; Physique mathématique [math-ph]; Combinatoire [math.CO]

Gérard Henry Edmond Duchamp, Silvia Goodenough, Karol A. Penson. Rational Hadamard products via Quantum Diagonal Operators. 2008. ⟨hal-00332398⟩