Extended finite operator calculus-an example of algebraization of analysis

• Autorzy: Andrzej Kwaśniewski , Ewa Borak
• Języki publikacji: EN

Abstrakty

EN

“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 same time this calculus is an example of the algebraization of the analysis-here restricted to the algebra of polynomials. Many of the results of ψ-calculus may be extended to Markowsky Q-umbral calculus where Q stands for a generalized difference operator, i.e. the one lowering the degree of any polynomial by one. This is a review article based on the recent first author contributions [1]. As the survey article it is supplemented by the short indicatory glossaries of notation and terms used by Ward [2], Viskov [7, 8], Markowsky [12], Roman [28–32] on one side and the Rota-oriented notation on the other side [9–11, 1, 3, 4, 35] (see also [33]).

Słowa kluczowe

EN

Extended umbral calculus; Graves-Heisenberg-Weyl algebra; 05A40; 81S99

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2004
• Tom: 2
• Numer: 5
• Strony: 767-792

Daty

wydano

2004-10-01

online

2004-10-01

Twórcy

autor

Andrzej Kwaśniewski

• Higher School of Mathematics and Applied Informatics

autor

Ewa Borak

• Białystok University

Bibliografia

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• [38] A.K. Kwaśniewski: “ψ-Appell polynomials' solutions of the-difference calculus nonhomogeneous equation”, Bull. Soc. Sci. Lett. Lodz, in print (ArXiv: math. CO/0405578 30 May 2004).
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Identyfikatory

DOI

10.2478/BF02475976