Identification of the theory of orthogonal polynomials in d-indeterminates with the theory of 3-diagonal symmetric interacting Fock spaces on ℂd

DOI10.1142/S0219025717500047zbMath1365.42019OpenAlexW2595605342MaRDI QIDQ2974264

Luigi Accardi, Ameur Dhahri, Abdessatar Barhoumi

Publication date: 6 April 2017

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

Full work available at URL: https://doi.org/10.1142/s0219025717500047

zbMATH Keywords

interacting Fock spaceFavard theoremmultidimensional orthogonal polynomialsquantum decomposition of a classical random variable

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Noncommutative probability and statistics (46L53)

Related Items (10)

d-dimensional orthogonal polynomials: Commutator theorem and other results ⋮ $$*$$ ∗ –Lie Algebras Canonically Associated to Probability Measures on $${\pmb {\varvec{\mathbb {R}}}}$$ R with All Moments ⋮ The quantum moment problem for a classical random variable and a classification of interacting Fock spaces ⋮ On the multi-dimensional Favard lemma ⋮ Quantum Markov chains: A unification approach ⋮ Orthogonal polynomial decomposition for random fields with all moments ⋮ Multivariate orthogonal polynomials: quantum decomposition, deficiency rank and support of measure ⋮ An information complexity index for probability measures on ℝ with all moments ⋮ The non-linear and quadratic quantization programs ⋮ Quantum walks on regular graphs with realizations in a system of anyons

Cites Work

• Orthogonal polynomials and special functions. Computation and applications. Lecture notes of the 5th European summer school, Madrid, Laganés, Spain, July 8--18, 2004
• Quasi-analytic vectors
• Orthogonal polynomials in two variables
• Moment problems in an infinite number of variables
• Recurrence relations, continued fractions, and orthogonal polynomials
• The Recursion Formulas for Orthogonal Polynomials innVariables
• Orthogonality and Recursion Formulas for Polynomials in n Variables
• Interacting Fock Spaces and Gaussianization of Probability Measures
• Unbounded Commuting Operators and Multivariate Orthogonal Polynomials
• CHARACTERIZATION OF PROBABILITY MEASURES THROUGH THE CANONICALLY ASSOCIATED INTERACTING FOCK SPACES
• MOMENTS AND COMMUTATORS OF PROBABILITY MEASURES
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