Finite-dimensional calculus

Philip Feinsilver (1) , René Schott (2, 3)

1 SIU - Southern Illinois University [Carbondale]
2 IECN - Institut Élie Cartan de Nancy
3 LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications

We develop finite-dimensional calculus using matrices. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin, and Arik who formulated it in terms of orthofermions. the matrix approach is used to implement our method of polynomial inversion in one-variable and multivariable settings. Here we establish notations, present some algebraic developments, and discuss the univariate case in detail.

Mots clés: inversion formulas; orthofermions; Heisenberg-Weyl algebra; polynomial systems

Domaines: Probabilités [math.PR]

Philip Feinsilver, René Schott. Finite-dimensional calculus. Journal of Physics A: Mathematical and Theoretical, 2009, 42, pp.375214. ⟨hal-00186130⟩