arXiv subjects

Piotr Multarzynski

Publications and source records attributed to Piotr Multarzynski.

2 recordsLinked to original sources

arXiv2010

D-polynomials and Taylor formula in quantum calculus

Quantum calculus based on the right invertible divided difference operator $D_{\sigma}^{\tau}$ is proposed here in context of algebraic analysis \cite{DPR}. The linear operator $D_{\sigma}^{\tau}$, specified with the help of two fixed maps $\sigma\;, \tau\colon M\rightarrow M$, generalizes the quantum derivative operator used in $h$- or $q$-calculus \cite{kac}. In the domain of $D_{\sigma}^{\tau}$ there are special elements defined as $D_{\sigma}^{\tau}$-polynomials and the corresponding Taylor formula is proved.

math.QA↗

arXiv2010

An algebraic analysis framework for quantum calculus

An algebraic analysis framework for quantum calculus is proposed. The quantum derivative operator $D_{\tau ,\sigma}$ is based on two commuting bijections $\tau$ and $\sigma$ defined on an arbitrary set $M$ equipped with a tension structure determined by a single tension function $\theta$, i.e. a 1-dimensional case is analyzed here. The well known cases, i.e. $h$- and $q$-calculi together with their symmetric versions, can be obtained owing to special choice of mappings $\tau$ and $\sigma$.

math.QA↗