On extended finite operator calculus of Rota and quantum groups. (English) Zbl 1022.39020
Summary: In this short note we state the existence of a natural and easy extension of classical operator calculus of Rota or equivalently – of umbral calculus of Roman-Rota and we indicate in brief its intrinsic relation to corresponding extensions of quantum harmonic oscillator-like models, i.e. corresponding extensions of Heisenberg-Weyl algebras.
MSC:
39A13 | Difference equations, scaling (\(q\)-differences) |
05A40 | Umbral calculus |
81S25 | Quantum stochastic calculus |
81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
Keywords:
extended umbral calculus; quantum \(q\)-plane; quantum harmonic oscillator; Heisenberg-Weyl algebrasReferences:
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