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arXiv · 1008.0672

An algebraic analysis framework for quantum calculus

Piotr Multarzynski
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Abstract

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 $\sigma$.

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BibTeXRIS

Piotr Multarzynski. 2010-07-27. An algebraic analysis framework for quantum calculus. https://arxiv.org/abs/1008.0672

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