Further remarks on extended umbral calculus. (English) Zbl 1018.05008

Kwaśniewski, A. K.; Grądzka, E.

Slovák, Jan (ed.) et al., The proceedings of the 21th winter school “Geometry and physics”, Srní, Czech Republic, January 13-20, 2001. Palermo: Circolo Matemàtico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 69, 117-130 (2002).

The paper deals with extensions of the finite operator calculus of G.-C. Rota called \(\psi\)-extensions which give a framework for corresponding quantum group investigations. This also covers the instance of the well-known \(q\)-analogue of umbral calculus. The article also contains glossaries of the most important terms and notations used by Ward, Viskov, Markowsky and Roman on one side and the Rota-oriented notations on the other side.
For the entire collection see [Zbl 0994.00029].

Reviewer: Peter Kirschenhofer (Leoben)

MSC:

05A40	Umbral calculus
81S99	General quantum mechanics and problems of quantization

Keywords:

umbral calculus; finite operator calculus