Displaying similar documents to “On deformations of finite operator calculus of Rota”

Extended finite operator calculus-an example of algebraization of analysis

Andrzej Kwaśniewski, Ewa Borak (2004)

Open Mathematics

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“A Calculus of Sequences” started in 1936 by Ward constitutes the general scheme for extensions of classical operator calculus of Rota-Mullin considered by many afterwards and after Ward. Because of the notation we shall call the Ward's calculus of sequences in its afterwards elaborated form-a ψ-calculus. The ψ-calculus in parts appears to be almost automatic, natural extension of classical operator calculus of Rota-Mullin or equivalently-of umbral calculus of Roman and Rota. At the...

More on deformed oscillator algebras and extended umbral calculus

Kwaśniewski, A. K., Grądzka, E.

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This paper deals with ϕ ( q ) calculus which is an extension of finite operator calculus due to Rota, and leading results of Rota’s calculus are easily ϕ -extendable. The particular case ϕ n ( q ) = [ n q 1 ] - 1 is known to be relevant for quantum group investigations. It is shown here that such ϕ ( q ) umbral calculus leads to infinitely many new ϕ -deformed quantum like oscillator algebra representations. The authors point to several references dealing with new applications of q umbral and ϕ ( q ) calculus in which new families...

Further remarks on extended umbral calculus

Kwaśniewski, A. K., Grądzka, E.

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The paper deals with extensions of the finite operator calculus of G.-C. Rota called ψ -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.