LOWERING AND RAISING OPERATORS FOR THE FREE MEIXNER CLASS OF ORTHOGONAL POLYNOMIALS

DOI10.1142/S0219025709003720zbMath1174.42030arXiv0812.0896OpenAlexW2009209055MaRDI QIDQ3643563

I. N. Rodionova, Eugene W. Lytvynov

Publication date: 9 November 2009

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0812.0896

zbMATH Keywords

Meixner class of orthogonal polynomialsfree Meixner class of orthogonal polynomials

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Related Items (1)

Meixner class of non-commutative generalized stochastic processes with freely independent values. II: The generating function

Cites Work

• Unnamed Item
• Processes with free increments
• Free martingale polynomials.
• Quadratic bosonic and free white noises.
• The Lévy-Itô decomposition in free probability
• Conditional moments of \(q\)-Meixner processes
• Renormalized squares of white noise and other non-Gaussian noises as Lévy processes on real Lie algebras
• Polynomials of Meixner's type in infinite dimensions: Jacobi fields and orthogonality measures
• Free Meixner states
• On a class of free Lévy laws related to a regression problem
• Orthogonal polynomials with a resolvent-type generating function

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