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Kwaśniewski, A. K.

On extended finite operator calculus of Rota and quantum groups. (English) Zbl 1022.39020

Integral Transforms Spec. Funct. 12, No. 4, 333-340 (2001).
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.

Cited in 1 Review
Cited in 3 Documents

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 algebras
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References:

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[3] DOI: 10.1088/0305-4470/22/18/004 · Zbl 0708.17015 · doi:10.1088/0305-4470/22/18/004
[4] DOI: 10.1088/0305-4470/22/21/020 · Zbl 0722.17009 · doi:10.1088/0305-4470/22/21/020
[5] DOI: 10.1142/S0217732390000287 · Zbl 1020.81649 · doi:10.1142/S0217732390000287
[6] DOI: 10.1088/0305-4470/24/11/004 · Zbl 0741.58017 · doi:10.1088/0305-4470/24/11/004
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[12] DOI: 10.1080/10652469608819093 · Zbl 0864.05007 · doi:10.1080/10652469608819093
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