Towards \(\psi\)-extension of Rota's finite operator calculus

DOI10.1016/S0034-4877(01)80092-6zbMath0994.05019arXivmath/0402078OpenAlexW3105523533MaRDI QIDQ5960836

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Publication date: 10 October 2002

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0402078

zbMATH Keywords

extended umbral calculusquantum \(q\)-planeRota's finite operator calculus

Mathematics Subject Classification ID

Umbral calculus (05A40) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Noncommutative geometry in quantum theory (81R60)

Related Items

An introduction to finite fibonomial calculus, Extended finite operator calculus -- an example of algebraization of analysis, On extended umbral calculus, oscillator-like algebras and generalized Clifford algebra, Main theorems of extended finite operator calculus

Cites Work

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• The theory of the umbral calculus. II
• The theory of the umbral calculus. III
• Sequences of functions of binomial type
• More on the umbral calculus, with emphasis on the \(q\)-umbral calculus
• Operatormethoden für q-identitäten
• Operatormethoden für q-Identitäten II: q-Laguerre-Polynome
• Operatormethoden für q-Identitäten. III: Umbrale Inversion und die Lagrangesche Formel
• A q-umbral calculus
• The theory of the umbral calculus. I
• Quantum Lie superalgebras and q-oscillators
• Differential operators and the theory of binomial enumeration
• The umbral calculus
• Quantum algebras and \(q\)-special functions related to coherent states maps of the disc
• On spectral properties of \(q\)-oscillator operators
• \(q\)-canonical commutation relations and stability of the Cuntz algebra
• \(q\)-orthogonal polynomials and the oscillator quantum group
• On the quantum group and quantum algebra approach to \(q\)-special functions
• Incidence functions as generalized arithmetic functions. I
• q-ANALOGUE OF BOSON COMMUTATOR AND THE QUANTUM GROUPS SU_q(2) AND SU_q(1, 1)
• On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)_q
• The q-deformed boson realisation of the quantum group SU(n)_qand its representations
• The quantum group SU_q(2) and a q-analogue of the boson operators
• On the q oscillator and the quantum algebra su_q(1,1)
• On quantization of simple harmonic oscillators
• Operator expansion in the derivative and multiplication byx
• More on the q-oscillator algebra and q-orthogonal polynomials
• Certain classes of arithmetic functions and the operation of additive convolution.
• On the Foundations of Combinatorial Theory IV Finite Vector Spaces and Eulerian Generating Functions
• On the Foundations of Combinatorial Theory V, Eulerian Differential Operators
• [https://portal.mardi4nfdi.de/wiki/Publication:5731810 On the foundations of combinatorial theory I. Theory of M�bius Functions]
• Über Polynome, die gleichzeitig zwei verschiedenen Orthogonalsystemen angehören
• Do the Equations of Motion Determine the Quantum Mechanical Commutation Relations?