On polynomials associated with Cauchy–Stieltjes kernel families

DOI10.1080/03610926.2022.2037647OpenAlexW4213335620MaRDI QIDQ6096171

Raouf Fakhfakh

Publication date: 11 September 2023

Published in: Communications in Statistics - Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03610926.2022.2037647

zbMATH Keywords

orthogonal polynomialsvariance functionCauchy-Stieltjes transformlowering and raising operators

Mathematics Subject Classification ID

Characteristic functions; other transforms (60E10) Free probability and free operator algebras (46L54)

Cites Work

• On Cauchy-Stieltjes kernel families
• One-sided Cauchy-Stieltjes kernel families
• On \(d\)-orthogonality of the Sheffer systems associated to a convolution semigroup
• Natural real exponential families with cubic variance functions
• Natural exponential families with quadratic variance functions
• Characterization of quadratic Cauchy-Stieltjes kernel families based on the orthogonality of polynomials
• The mean of the reciprocal in a Cauchy-Stieltjes family
• Variance function of Boolean additive convolution
• On some properties of Cauchy-Stieltjes kernel families
• Characterizations of some polynomial variance functions by \(d\)-pseudo-orthogonality
• FREE EXPONENTIAL FAMILIES AS KERNEL FAMILIES
• The jacobi inversion formula
• BOOLEAN MULTIPLICATIVE CONVOLUTION AND CAUCHY-STIELTJES KERNEL FAMILIES
• Cauchy–Stieltjes families with polynomial variance functions and generalized orthogonality
• Explicit free multiplicative law of large numbers

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