Polynomials in algebraic analysis
Abstract
The concept of polynomials in the sense of algebraic analysis, for a single right invertible linear operator, was introduced and studied originally by D. Przeworska-Rolewicz \cite{DPR}. One of the elegant results corresponding with that notion is a purely algebraic version of the Taylor formula, being a generalization of its usual counterpart, well known for functions of one variable. In quantum calculus there are some specific discrete derivations analyzed, which are right invertible linear operators \cite{kac}. Hence, with such quantum derivations one can associate the corresponding concept of algebraic polynomials and consequently the quantum calculus version of Taylor formula \cite{MULT2}. In the present paper we define and analyze, in the sense of algebraic analysis, polynomials corresponding with a given family of right invertible operators. Within this approach we generalize the usual polynomials of several variables.
Cite
@article{arxiv.1201.1026,
title = {Polynomials in algebraic analysis},
author = {Piotr Multarzyński},
journal= {arXiv preprint arXiv:1201.1026},
year = {2012}
}
Comments
arXiv admin note: text overlap with arXiv:1012.2611